Automatic and Hyperbolic Groups
- Introduction
- Automatic Groups
- Construction of an Automatic Group
- Modifying Limits
- Accessing Group Information
- Properties of an Automatic Group
- Constructing Words
- Operations on Elements
u * v: GrpRWSElt, GrpRWSElt → GrpRWSEltu / v: GrpRWSElt, GrpRWSElt → GrpRWSEltu ^ n: GrpRWSElt, RngIntElt → GrpRWSEltu ^ v: GrpRWSElt, GrpRWSElt → GrpRWSEltInverse(w): GrpRWSElt → GrpRWSElt(u, v): GrpRWSElt, GrpRWSElt → GrpRWSElt(u₁, ..., uᵣ): GrpRWSElt, ..., GrpRWSElt → GrpRWSEltu eq v: GrpRWSElt, GrpRWSElt → BoolEltu ne v: GrpRWSElt, GrpRWSElt → BoolEltIsId(w): GrpRWSElt → BoolEltIsIdentity(w): GrpRWSElt → BoolElt# u: GrpRWSElt → RngIntEltElementToSequence(u): GrpRWSElt → [ RngIntElt ]Eltseq(u): GrpRWSElt → [ RngIntElt ]- Example: Word Operations in an Automatic Group
- Set Operations
Random(G, n): GrpAtc, RngIntElt → GrpAtcEltRandom(G): GrpAtc → GrpAtcEltRepresentative(G): GrpAtc → GrpAtcEltRep(G): GrpAtc → GrpAtcEltSet(G, a, b): GrpAtc, RngIntElt, RngIntElt → SetEnumSet(G): GrpAtc → SetEnumSeq(G, a, b): GrpAtc, RngIntElt, RngIntElt → SeqEnumSeq(G): GrpAtc → SeqEnum- Example: Set Operations on a Dihedral Group
- Homomorphisms
- The Growth Function
- Hyperbolic Groups
- Bibliography