Identification

Subsections

• Identification as an Abstract Group
• Identification as a Permutation Group

Identification as an Abstract Group

NameSimple(G) : GrpPerm -> <RngIntElt, RngIntElt, RngIntElt>

Given a simple group G, determine the isomorphism type of G. The type is returned in the form of a triple of three integers f, d and q, where the interpretation of these integers is that given in the description of the function CompositionFactors.

Identification as a Permutation Group

The first functions described in this subsection detect whether or not a permutation group is alternating or symmetric in its natural representation. They are based on the algorithm "Detect Alternating" outlined [CB92].

IsAlternating(G) : GrpPerm -> BoolElt

True if the permutation group G defined as acting on X is the alternating group Alt(X).

IsSymmetric(G) : GrpPerm -> BoolElt

True if the permutation group G defined as acting on X is the symmetric group Sym(X).

IsAltsym(G) : GrpPerm -> BoolElt

True if the permutation group G defined as acting on X contains the alternating group Alt(X).

TwoTransitiveGroupIdentification(G) : GrpPerm -> Tup

Given a 2-transitive group G, return a tuple giving the abstract isomorphism type of the group. This is an implementation of the method of Cameron and Cannon [CC91].