Primitivity Properties on Coset Geometries
- IsPrimitive(C): CosetGeom -> BoolElt
- IsPRI(C): CosetGeom -> BoolElt
- IsPrimitive(C): CosetGeom -> BoolElt
- IsPRI(C): CosetGeom -> BoolElt
Given a coset geometry \(C\), this function returns the boolean value
trueif and only if \(C\) is a primitive geometry, i.e. all of its maximal parabolic subgroups are maximal subgroups of its group.
- IsWeaklyPrimitive(C): CosetGeom -> BoolElt
- IsWPRI(C): CosetGeom -> BoolElt
- IsWeaklyPrimitive(C): CosetGeom -> BoolElt
- IsWPRI(C): CosetGeom -> BoolElt
Given a coset geometry \(C\), this function returns the boolean value
trueif and only if \(C\) is a weakly primitive geometry, i.e. at least one of its maximal parabolic subgroups is a maximal subgroup of its group.
- IsResiduallyPrimitive(C): CosetGeom -> BoolElt
- IsRPRI(C): CosetGeom -> BoolElt
- IsResiduallyPrimitive(C): CosetGeom -> BoolElt
- IsRPRI(C): CosetGeom -> BoolElt
Given a coset geometry \(C\), this function returns the boolean value
trueif and only if \(C\) is a primitive geometry and all of its residues are as well.
- IsResiduallyWealyPrimitive(C): CosetGeom -> BoolElt
- IsRWPRI(C): CosetGeom -> BoolElt
- IsRWP(C): CosetGeom -> BoolElt
- IsResiduallyWeaklyPrimitive(C): CosetGeom -> BoolElt
- IsRWPRI(C): CosetGeom -> BoolElt
- IsRWP(C): CosetGeom -> BoolElt
Given a coset geometry \(C\), this function returns the boolean value
trueif and only if \(C\) is a weakly primitive geometry and all of its residues are as well.
- IsLocallyTwoTransitive(C): CosetGeom -> BoolElt
- Is2T1(C): CosetGeom -> BoolElt
Given a coset geometry \(C\), this function returns the boolean value
trueif and only if \(C\) is locally two-transitive, i.e. all of its minimal parabolic subgroups have a two-transitive action on the cosets of the Borel subgroup.
- LocallySArcTransitive(C): CosetGeom -> RngIntElt
Given a coset geometry \(C\), this function returns the largest integer \(s\) such that \(C\) is locally \(s\)-arc-transitive but not locally \((s+1)\)-arc-transitive. If the function returns 10, it means \(C\) is a coset geometry corresponding to a polygon and hence this value must be considered as infinity.