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.