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 true if 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 true if 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 true if 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 true if 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 true if 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.