Subsections

• Matrix Group Predicates
• Abstract Group Predicates

True if the matrix group G of degree n over the field K is the general linear group GL(n, K).

True if the matrix group G of degree n over the field K is the special linear group SL(n, K).

True if the matrix group G of degree n over the field K contains the special linear group SL(n, K).

Given a matrix group G, return true if G acts irreducibly on its natural module.

True if the group G is abelian, false otherwise.

True if the group G is cyclic, false otherwise.

True if the group G is elementary abelian, false otherwise.

True if the subgroup H of the group G lies in the centre of G, false otherwise.

Given a group G and elements g and h belonging to G, return the value true if g and h are conjugate in G. The function returns a second value in the event that the elements are conjugate: an element k which conjugates g into h.

[Future release] IsConjugate(G, H, K) : GrpMat, GrpMat, GrpMat -> BoolElt, GrpMatElt | Unass

Given a group G and subgroups H and K belonging to G, return the value true if G and H are conjugate in G. The function returns a second value in the event that the subgroups are conjugate: an element z which conjugates H into K.

True if the subgroup H of the group G is a maximal subgroup of G. This function is evaluated by constructing the permutation representation of G on the cosets of H and testing this representation for primitivity. For this reason, the use of IsMaximal should be avoided if the index of H in G exceeds a few thousand.

True if the group G is nilpotent, false otherwise.

True if the subgroup H of the group G is a normal subgroup of G, false otherwise.

True if the group G is perfect, false otherwise.

True if the subgroup H of the group G is self-normalizing in G, false otherwise.

True if the group G is simple, false otherwise.

IsSolvable(G) : GrpMat -> BoolElt

True if the group G is soluble, false otherwise.

True if the subgroup H of the group G is subnormal in G, false otherwise.