# Matrix Groups over Finite Fields

- [Introduction](introduction.md)

- [Finding Elements with Prescribed Properties](element-order.md)

  - [`RandomElementOfOrder(G, n : parameters): GrpMat, RngIntElt → BoolElt, GrpMatElt, GrpSLPElt, BoolElt`](element-order.md#function-randomelementoforder-grpmat-rngintelt)

  - [`RandomElementOfNormalClosure(G, N): Grp → GrpElt`](element-order.md#function-randomelementofnormalclosure-grp)

  - [`InvolutionClassicalGroupEven(G : parameters): GrpMat[FldFin] → GrpMatElt[FldFin], GrpSLPElt, RngIntElt`](element-order.md#function-involutionclassicalgroupeven-grpmat-fldfin)

- [Monte Carlo Algorithms for Subgroups](monte-carlo.md)

  - [`CentraliserOfInvolution(G, g : parameters): GrpMat, GrpMatElt → GrpMat`](monte-carlo.md#function-centraliserofinvolution-grpmat-grpmatelt)

  - [`CentraliserOfInvolution(G, g, w : parameters): GrpMat, GrpMatElt, GrpSLPElt → GrpMat, []`](monte-carlo.md#function-centraliserofinvolution-grpmat-grpmatelt-grpslpelt)

  - [`AreInvolutionsConjugate({G, x, wx, y,}{ wy : parameters}): GrpMat, GrpMatElt, GrpSLPElt, GrpMatElt, GrpSLPElt → BoolElt, GrpMatElt, GrpSLPElt`](monte-carlo.md#function-areinvolutionsconjugate-grpmat-grpmatelt-grpslpelt-grpmatelt-grpslpelt)

  - [`NormalClosureMonteCarlo(G, H ): GrpMat, GrpMat → GrpMat`](monte-carlo.md#function-normalclosuremontecarlo-grpmat-grpmat)

  - [`NormalClosureMonteCarlo(G, H : parameters): GrpPerm, GrpPerm → GrpMat`](monte-carlo.md#function-normalclosuremontecarlo-grpperm-grpperm)

  - [`DerivedGroupMonteCarlo(G : parameters): GrpMat → GrpMat`](monte-carlo.md#function-derivedgroupmontecarlo-grpmat)

  - [`IsProbablyPerfect(G : parameters): Grp → BoolElt`](monte-carlo.md#function-isprobablyperfect-grp)

  - [`Example: Is Probably Perfect`](monte-carlo.md#example-ex-00c3d9)

- [Aschbacher Reduction](aschbacher-reduction.md)

  - [Introduction](aschbacher-reduction.md#introduction)

  - [Primitivity](aschbacher-reduction.md#primitivity)

    - [`IsPrimitive(G: parameters): GrpMat → BoolElt`](aschbacher-reduction.md#function-isprimitive-grpmat)

    - [`ImprimitiveBasis(G): GrpMat → SeqEnum`](aschbacher-reduction.md#function-imprimitivebasis-grpmat)

    - [`Blocks(G): GrpMat → SeqEnum`](aschbacher-reduction.md#function-blocks-grpmat)

    - [`BlocksImage(G): GrpMat → GrpPerm`](aschbacher-reduction.md#function-blocksimage-grpmat)

    - [`ImprimitiveAction(G, g): GrpMat, GrpMatElt → GrpPermElt`](aschbacher-reduction.md#function-imprimitiveaction-grpmat-grpmatelt)

    - [`Example: Is Primitive`](aschbacher-reduction.md#example-ex-cc4edb)

  - [Semilinearity](aschbacher-reduction.md#semilinearity)

    - [`IsSemiLinear(G): GrpMat → BoolElt`](aschbacher-reduction.md#function-issemilinear-grpmat)

    - [`DegreeOfFieldExtension(G): GrpMat → RngIntElt`](aschbacher-reduction.md#function-degreeoffieldextension-grpmat)

    - [`CentralisingMatrix(G): GrpMat → AlgMatElt`](aschbacher-reduction.md#function-centralisingmatrix-grpmat)

    - [`FrobeniusAutomorphisms(G): GrpMat → SeqEnum`](aschbacher-reduction.md#function-frobeniusautomorphisms-grpmat)

    - [`WriteOverLargerField(G): GrpMat → GrpMat, GrpAb, SeqEnum`](aschbacher-reduction.md#function-writeoverlargerfield-grpmat)

    - [`Example: Semilinearity`](aschbacher-reduction.md#example-ex-0459a8)

  - [Tensor Products](aschbacher-reduction.md#tensor-products)

    - [`IsTensor(G: parameters): GrpMat → BoolElt`](aschbacher-reduction.md#function-istensor-grpmat)

    - [`TensorBasis(G): GrpMat → GrpMatElt`](aschbacher-reduction.md#function-tensorbasis-grpmat)

    - [`TensorFactors(G): GrpMat → GrpMat, GrpMat`](aschbacher-reduction.md#function-tensorfactors-grpmat)

    - [`IsProportional(X, k): Mtrx, RngIntElt → BoolElt, Tup`](aschbacher-reduction.md#function-isproportional-mtrx-rngintelt)

    - [`Example: Tensor`](aschbacher-reduction.md#example-ex-8c10fc)

  - [Tensor-induced Groups](aschbacher-reduction.md#tensor-induced-groups)

    - [`IsTensorInduced(G : parameters): GrpMat → BoolElt`](aschbacher-reduction.md#function-istensorinduced-grpmat)

    - [`TensorInducedBasis(G): GrpMat → GrpMatElt`](aschbacher-reduction.md#function-tensorinducedbasis-grpmat)

    - [`TensorInducedPermutations(G): GrpMat → SeqEnum`](aschbacher-reduction.md#function-tensorinducedpermutations-grpmat)

    - [`TensorInducedAction(G, g): GrpMat, GrpMatElt → GrpPermElt`](aschbacher-reduction.md#function-tensorinducedaction-grpmat-grpmatelt)

    - [`Example: Tensor Induced`](aschbacher-reduction.md#example-ex-1ef8b8)

  - [Normalisers of Extraspecial $r$-groups and Symplectic 2-groups](aschbacher-reduction.md#normalisers-of-extraspecial-r-groups-and-symplectic-2-groups)

    - [`IsExtraSpecialNormaliser(G): GrpMat → BoolElt`](aschbacher-reduction.md#function-isextraspecialnormaliser-grpmat)

    - [`ExtraSpecialParameters(G): GrpMat → [RngIntElt, RngIntElt]`](aschbacher-reduction.md#function-extraspecialparameters-grpmat)

    - [`ExtraSpecialGroup(G): GrpMat → GrpMat`](aschbacher-reduction.md#function-extraspecialgroup-grpmat)

    - [`ExtraSpecialNormaliser(G): GrpMat → SeqEnum`](aschbacher-reduction.md#function-extraspecialnormaliser-grpmat)

    - [`ExtraSpecialAction(G, g): GrpMat, GrpMatElt → GrpMatElt`](aschbacher-reduction.md#function-extraspecialaction-grpmat-grpmatelt)

    - [`ExtraSpecialBasis(G): GrpMat → GrpMatElt`](aschbacher-reduction.md#function-extraspecialbasis-grpmat)

    - [`Example: Extra Special Normaliser`](aschbacher-reduction.md#example-ex-2adbb0)

  - [Writing Representations over Subfields](aschbacher-reduction.md#writing-representations-over-subfields)

    - [`IsOverSmallerField(G : parameters): GrpMat → BoolElt, GrpMat`](aschbacher-reduction.md#function-isoversmallerfield-grpmat)

    - [`IsOverSmallerField(G, k : parameters): GrpMat → BoolElt, GrpMat`](aschbacher-reduction.md#function-isoversmallerfield-grpmat-2)

    - [`SmallerField(G): GrpMat → FLdFin`](aschbacher-reduction.md#function-smallerfield-grpmat)

    - [`SmallerFieldBasis(G): GrpMat → GrpMatElt`](aschbacher-reduction.md#function-smallerfieldbasis-grpmat)

    - [`SmallerFieldImage(G, g): GrpMat, GrpMatElt → GrpMatElt`](aschbacher-reduction.md#function-smallerfieldimage-grpmat-grpmatelt)

    - [`Example: Is Over Smaller Field`](aschbacher-reduction.md#example-ex-3b0781)

    - [`WriteOverSmallerField(G, F): GrpMat, FldFin → GrpMat, Map`](aschbacher-reduction.md#function-writeoversmallerfield-grpmat-fldfin)

    - [`Example: Write Over Smaller Field`](aschbacher-reduction.md#example-ex-c2e1e0)

  - [Decompositions with Respect to a Normal Subgroup](aschbacher-reduction.md#decompositions-with-respect-to-a-normal-subgroup)

    - [`SearchForDecomposition(G, S): GrpMat, [GrpMatElt] → BoolElt`](aschbacher-reduction.md#function-searchfordecomposition-grpmat-grpmatelt)

    - [Accessing the Decomposition Information](aschbacher-reduction.md#accessing-the-decomposition-information)

      - [`Example: Decompose`](aschbacher-reduction.md#example-ex-14d37b)

- [Constructive Recognition for Simple Groups](natural-copy-classical.md)

  - [Constructive Recognition for Classical Groups](natural-copy-classical.md#constructive-recognition-for-classical-groups)

    - [`ClassicalStandardGenerators(type, d, q): MonStgElt, RngIntElt, RngIntElt → []`](natural-copy-classical.md#function-classicalstandardgenerators-monstgelt-rngintelt-rngintelt)

    - [`ClassicalConstructiveRecognition(G, type, d, q): GrpMat[FldFin], MonStgElt, RngIntElt, RngIntElt → BoolElt, Map, Map, Map, Map, SeqEnum, SeqEnum`](natural-copy-classical.md#function-classicalconstructiverecognition-grpmat-fldfin-monstgelt-rngintelt-rngintelt)

    - [`ClassicalConstructiveRecognition(G): GrpMat[FldFin] → BoolElt, SeqEnum, SeqEnum`](natural-copy-classical.md#function-classicalconstructiverecognition-grpmat-fldfin)

    - [`Example: Classical Constructive Recognition`](natural-copy-classical.md#example-ex-0be2ca)

    - [`ClassicalChangeOfBasis(G): GrpMat[FldFin] → GrpMatElt[FldFin]`](natural-copy-classical.md#function-classicalchangeofbasis-grpmat-fldfin)

    - [`ClassicalRewrite({G, gens, type, dim,}{ q, g : parameters}): Grp, SeqEnum, MonStgElt, RngIntElt, RngIntElt, GrpElt → BoolElt, GrpElt`](natural-copy-classical.md#function-classicalrewrite-grp-seqenum-monstgelt-rngintelt-rngintelt-grpelt)

    - [`ClassicalRewriteNatural(type, CB, g): MonStgElt, GrpMatElt, GrpMatElt → BoolElt, GrpElt`](natural-copy-classical.md#function-classicalrewritenatural-monstgelt-grpmatelt-grpmatelt)

    - [`ClassicalRewriteNatural({G, type, }{CB, g}): MonStgElt, GrpMatElt, GrpMatElt → BoolElt, GrpElt`](natural-copy-classical.md#function-classicalrewritenatural-monstgelt-grpmatelt-grpmatelt-2)

    - [`ClassicalStandardPresentation(type, d, q : parameters): MonStgElt, RngIntElt, RngIntElt → SLPGroup, []`](natural-copy-classical.md#function-classicalstandardpresentation-monstgelt-rngintelt-rngintelt)

    - [`Example: Classical Constructive Recognition`](natural-copy-classical.md#example-ex-7ccc3b)

  - [Constructive Recognition for Exceptional Groups](natural-copy-classical.md#constructive-recognition-for-exceptional-groups)

    - [`ExceptionalStandardGenerators(type, rank, q): MonStgElt, RngIntElt, RngIntElt → []`](natural-copy-classical.md#function-exceptionalstandardgenerators-monstgelt-rngintelt-rngintelt)

    - [`ExceptionalConstructiveRecognition(G, type, rank, q): GrpMat[FldFin], MonStgElt, RngIntElt, RngIntElt → BoolElt, Map, Map, Map, Map, SeqEnum, SeqEnum`](natural-copy-classical.md#function-exceptionalconstructiverecognition-grpmat-fldfin-monstgelt-rngintelt-rngintelt)

    - [`Example: Exceptional Constructive Recognition`](natural-copy-classical.md#example-ex-111a3c)

    - [`ExceptionalRewrite(type, rank, q, X, Xm, g): MonStgElt, RngIntElt, RngIntElt, SeqEnum, SeqEnum, GrpElt → BoolElt, GrpElt`](natural-copy-classical.md#function-exceptionalrewrite-monstgelt-rngintelt-rngintelt-seqenum-seqenum-grpelt)

    - [`ExceptionalStandardPresentation(type, rank, q): MonStgElt, RngIntElt, RngIntElt → SLPGroup, []`](natural-copy-classical.md#function-exceptionalstandardpresentation-monstgelt-rngintelt-rngintelt)

    - [`Example: Exp Standard`](natural-copy-classical.md#example-ex-b84999)

- [Composition Trees for Matrix Groups](composition-tree.md)

  - [The Composition Tree Algorithm](composition-tree.md#the-composition-tree-algorithm)

  - [Constructing the Composition Tree](composition-tree.md#constructing-the-composition-tree)

    - [`CompositionTree(G): GrpMat[FldFin] → []`](composition-tree.md#function-compositiontree-grpmat-fldfin)

    - [`Example: Composition Tree`](composition-tree.md#example-ex-009621)

    - [`CompositionTree(G : parameters): GrpMat[FldFin] → []`](composition-tree.md#function-compositiontree-grpmat-fldfin-2)

    - [`CompositionTreeFastVerification(G): Grp → BoolElt`](composition-tree.md#function-compositiontreefastverification-grp)

    - [`CompositionTreeVerify(G): Grp → BoolElt, []`](composition-tree.md#function-compositiontreeverify-grp)

    - [`Example: Composition Tree Verify`](composition-tree.md#example-ex-1c147a)

  - [Accessing the Composition Tree](composition-tree.md#accessing-the-composition-tree)

    - [`CompositionTreeOrder(G): Grp → RngIntElt`](composition-tree.md#function-compositiontreeorder-grp)

    - [`CompositionTreeNonAbelianFactors(G): Grp → RngIntElt`](composition-tree.md#function-compositiontreenonabelianfactors-grp)

    - [`DisplayCompTreeNodes(G : parameters): Grp`](composition-tree.md#function-displaycomptreenodes-grp)

    - [`Example: Comp Tree J4`](composition-tree.md#example-ex-8acf9e)

    - [`CompositionTreeNiceGroup(G): Grp → GrpMat[FldFin]`](composition-tree.md#function-compositiontreenicegroup-grp)

    - [`CompositionTreeSLPGroup(G): Grp → GrpSLP, Map`](composition-tree.md#function-compositiontreeslpgroup-grp)

    - [`CompositionTreeNiceToUser(G): Grp → Map, []`](composition-tree.md#function-compositiontreenicetouser-grp)

    - [`CompositionTreeOrder(G): Grp → RngIntElt`](composition-tree.md#function-compositiontreeorder-grp-2)

    - [`CompositionTreeFactoredOrder(G): Grp → RngIntEltFact`](composition-tree.md#function-compositiontreefactoredorder-grp)

    - [`CompositionTreeElementToWord(G, g): Grp, GrpElt → BoolElt, GrpSLPElt`](composition-tree.md#function-compositiontreeelementtoword-grp-grpelt)

    - [`CompositionTreeNonAbelianFactors(G): GrpMat[FldFin] → List`](composition-tree.md#function-compositiontreenonabelianfactors-grpmat-fldfin)

    - [`CompositionTreeCBM(G): GrpMat[FldFin → GrpMatElt`](composition-tree.md#function-compositiontreecbm-grpmat-fldfin)

    - [`CompositionTreeReductionInfo(G, t): Grp, RngIntElt → MonStgElt, Grp, Grp`](composition-tree.md#function-compositiontreereductioninfo-grp-rngintelt)

    - [`CompositionTreeSeries(G): Grp → SeqEnum, List, List, List, BoolElt, []`](composition-tree.md#function-compositiontreeseries-grp)

    - [`CompositionTreeFactorNumber(G, g): Grp, GrpElt → RngIntElt`](composition-tree.md#function-compositiontreefactornumber-grp-grpelt)

    - [`HasCompositionTree(G): Grp → BoolElt`](composition-tree.md#function-hascompositiontree-grp)

    - [`CleanCompositionTree(G): Grp`](composition-tree.md#function-cleancompositiontree-grp)

    - [`Example: Comp Tree1`](composition-tree.md#example-ex-0bfaff)

    - [`Example: Comp Tree2`](composition-tree.md#example-ex-b767f8)

- [The LMG functions](LMG.md)

  - [`SetLMGSchreierBound(n): RngIntElt`](LMG.md#function-setlmgschreierbound-rngintelt)

  - [`LMGInitialize(G : parameters): GrpMat`](LMG.md#function-lmginitialize-grpmat)

  - [`LMGInitialise(G : parameters): GrpMat`](LMG.md#function-lmginitialise-grpmat)

  - [`LMGOrder(G): GrpMat[FldFin] → RngIntElt`](LMG.md#function-lmgorder-grpmat-fldfin)

  - [`LMGFactoredOrder(G): GrpMat[FldFin] → SeqEnum`](LMG.md#function-lmgfactoredorder-grpmat-fldfin)

  - [`LMGIsIn(G, x): GrpMat, GrpMatElt → BoolElt, GrpSLPElt`](LMG.md#function-lmgisin-grpmat-grpmatelt)

  - [`LMGIsSubgroup(G, H): GrpMat, GrpMat → BoolElt`](LMG.md#function-lmgissubgroup-grpmat-grpmat)

  - [`LMGEqual(G, H): GrpMat, GrpMat → BoolElt`](LMG.md#function-lmgequal-grpmat-grpmat)

  - [`LMGIndex(G, H): GrpMat, GrpMat → RngIntElt`](LMG.md#function-lmgindex-grpmat-grpmat)

  - [`LMGIsNormal(G, H): GrpMat, GrpMat → BoolElt`](LMG.md#function-lmgisnormal-grpmat-grpmat)

  - [`LMGNormalClosure(G, H): GrpMat, GrpMat → GrpMat`](LMG.md#function-lmgnormalclosure-grpmat-grpmat)

  - [`LMGDerivedGroup(G): GrpMat → GrpMat`](LMG.md#function-lmgderivedgroup-grpmat)

  - [`LMGCommutatorSubgroup(G, H): GrpMat, GrpMat → GrpMat`](LMG.md#function-lmgcommutatorsubgroup-grpmat-grpmat)

  - [`LMGIsSoluble(G): GrpMat → BoolElt`](LMG.md#function-lmgissoluble-grpmat)

  - [`LMGIsSolvable(G): GrpMat → BoolElt`](LMG.md#function-lmgissolvable-grpmat)

  - [`LMGIsNilpotent(G): GrpMat → BoolElt`](LMG.md#function-lmgisnilpotent-grpmat)

  - [`LMGCompositionSeries(G): GrpMat[FldFin] → SeqEnum`](LMG.md#function-lmgcompositionseries-grpmat-fldfin)

  - [`LMGCompositionFactors(G): GrpMat[FldFin] → SeqEnum`](LMG.md#function-lmgcompositionfactors-grpmat-fldfin)

  - [`LMGChiefSeries(G): GrpMat[FldFin] → SeqEnum`](LMG.md#function-lmgchiefseries-grpmat-fldfin)

  - [`LMGChiefFactors(G): GrpMat[FldFin] → SeqEnum`](LMG.md#function-lmgchieffactors-grpmat-fldfin)

  - [`LMGUnipotentRadical(G): GrpMat → GrpMat, GrpPC, Map`](LMG.md#function-lmgunipotentradical-grpmat)

  - [`LMGSolubleRadical(G): GrpMat → GrpMat, GrpPC, Map`](LMG.md#function-lmgsolubleradical-grpmat)

  - [`LMGSolvableRadical(G): GrpMat → GrpMat, GrpPC, Map`](LMG.md#function-lmgsolvableradical-grpmat)

  - [`LMGFittingSubgroup(G): GrpMat → GrpMat, GrpPC, Map`](LMG.md#function-lmgfittingsubgroup-grpmat)

  - [`LMGCentre(G): GrpMat → GrpMat`](LMG.md#function-lmgcentre-grpmat)

  - [`LMGCenter(G): GrpMat → GrpMat`](LMG.md#function-lmgcenter-grpmat)

  - [`LMGSylow(G,p): GrpMat, RngIntElt → GrpMat`](LMG.md#function-lmgsylow-grpmat-rngintelt)

  - [`LMGSocleStar(G): GrpMat → GrpMat`](LMG.md#function-lmgsoclestar-grpmat)

  - [`LMGSocleStarFactors(G): GrpMat → SeqEnum, SeqEnum`](LMG.md#function-lmgsoclestarfactors-grpmat)

  - [`LMGSocleStarAction(G): GrpMat → Map, GrpPerm, GrpMat`](LMG.md#function-lmgsoclestaraction-grpmat)

  - [`LMGSocleStarActionKernel(G): GrpMat → GrpMat, GrpPC, Map`](LMG.md#function-lmgsoclestaractionkernel-grpmat)

  - [`LMGSocleStarQuotient(G): GrpMat → GrpPerm, Map, GrpMat`](LMG.md#function-lmgsoclestarquotient-grpmat)

  - [`Example: LM Gex`](LMG.md#example-ex-533478)

  - [`LMGRadicalQuotient(G): GrpMat → GrpPerm, Map, GrpMat`](LMG.md#function-lmgradicalquotient-grpmat)

  - [`LMGCentraliser(G, g): GrpMat, GrpMatElt → GrpMat`](LMG.md#function-lmgcentraliser-grpmat-grpmatelt)

  - [`LMGCentralizer(G, g): GrpMat, GrpMatElt → GrpMat`](LMG.md#function-lmgcentralizer-grpmat-grpmatelt)

  - [`LMGIsConjugate(G, g, h): GrpMat, GrpMatElt, GrpMatElt → BoolElt, GrpMatElt`](LMG.md#function-lmgisconjugate-grpmat-grpmatelt-grpmatelt)

  - [`LMGClasses(G): GrpMat → SeqEnum`](LMG.md#function-lmgclasses-grpmat)

  - [`LMGConjugacyClasses(G): GrpMat → SeqEnum`](LMG.md#function-lmgconjugacyclasses-grpmat)

  - [`LMGNormaliser(G, H): GrpMat, GrpMat → GrpMat`](LMG.md#function-lmgnormaliser-grpmat-grpmat)

  - [`LMGNormalizer(G, H): GrpMat, GrpMat → GrpMat`](LMG.md#function-lmgnormalizer-grpmat-grpmat)

  - [`LMGIsConjugate(G, H, K): GrpMat, GrpMat, GrpMat → BoolElt, GrpMatElt`](LMG.md#function-lmgisconjugate-grpmat-grpmat-grpmat)

  - [`LMGMeet(G, H, K): GrpMat, GrpMat, GrpMat → GrpMat`](LMG.md#function-lmgmeet-grpmat-grpmat-grpmat)

  - [`LMGMaximalSubgroups(G): GrpMat → SeqEnum`](LMG.md#function-lmgmaximalsubgroups-grpmat)

  - [`LMGNormalSubgroups(G): GrpMat → SeqEnum`](LMG.md#function-lmgnormalsubgroups-grpmat)

  - [`LMGLowIndexSubgroups(G,n): GrpMat, RngIntElt → SeqEnum`](LMG.md#function-lmglowindexsubgroups-grpmat-rngintelt)

  - [`LMGCosetAction(G,H : parameters): GrpMat, GrpMat → Map, GrpPerm, GrpMat`](LMG.md#function-lmgcosetaction-grpmat-grpmat)

  - [`LMGCosetImage(G,H): GrpMat, GrpMat → GrpPerm`](LMG.md#function-lmgcosetimage-grpmat-grpmat)

  - [`LMGCosetActionInverseImage(G, f, i): GrpMat, Map, RngIntElt → GrpMatElt`](LMG.md#function-lmgcosetactioninverseimage-grpmat-map-rngintelt)

  - [`LMGRightTransversal(G,H : parameters): GrpMat, GrpMat → SeqEnum`](LMG.md#function-lmgrighttransversal-grpmat-grpmat)

  - [`LMGIsPrimitive(G): GrpMat → BoolElt`](LMG.md#function-lmgisprimitive-grpmat)

  - [`LMGCharacterTable(G : parameters): GrpMat → SeqEnum`](LMG.md#function-lmgcharactertable-grpmat)

  - [`Example: LM Gex2`](LMG.md#example-ex-fa2be2)

- [Finding a Base](findbase.md)

  - [`LMGBase(G : parameters): GrpMat → Tup, SeqEnum, SeqEnum`](findbase.md#function-lmgbase-grpmat)

  - [`Example: base`](findbase.md#example-ex-c9a7be)

- [Unipotent Matrix Groups](UnipPC.md)

  - [`UnipotentMatrixGroup(G): GrpMat → GrpMatUnip`](UnipPC.md#function-unipotentmatrixgroup-grpmat)

  - [`WordMap(G): GrpMatUnip → Map`](UnipPC.md#function-wordmap-grpmatunip)

  - [`Example: Unip PC Word Map`](UnipPC.md#example-ex-30af78)

  - [`PCPresentation(G): GrpMatUnip → GrpPC, Map, Map`](UnipPC.md#function-pcpresentation-grpmatunip)

  - [`Order(G): GrpMatUnip → RngIntElt`](UnipPC.md#function-order-grpmatunip)

  - [`# G: GrpMatUnip → RngIntElt`](UnipPC.md#operation-operation-grpmatunip-rngintelt)

  - [`FactoredOrder(G): GrpMatUnip → [ <RngIntElt, RngIntElt> ]`](UnipPC.md#function-factoredorder-grpmatunip)

  - [`g in G: GrpMatElt, GrpMatUnip → BoolElt`](UnipPC.md#operation-op-in-grpmatelt-grpmatunip)

  - [`Example: Unip PC Pres`](UnipPC.md#example-ex-f568e8)