The functions described in this section apply only to finite groups for which a base and strong generating set may be constructed.
Construct a polycyclic generating sequence for the soluble group G.
Given a soluble group G, construct a group S in category GrpPC, isomorphic to G. In addition to returning S, the function returns an isomorphism φ: G -> S.
Given a soluble group G, and a prime p dividing |G|, return the lower p-central series for G. The series is returned as a sequence of subgroups.
Given a p-group G, return true if G is special, false otherwise.
Given a p-group G, return true if G is extraspecial, false otherwise.
Given a p-group G, return the Frattini subgroup.
Given a p-group G, return the Jennings series for G. The series is returned as a sequence of subgroups.
Given an abelian group G, return a sequence Q containing the types of each p-primary component of G. The non-primary form gives the Smith form invariants, i.e. each element of the sequence divides the next.
Given an abelian group G, return sequences B and I, where I are p-primary invariants for G, and B are generators for G having the orders in I. The non-primary form uses the Smith form invariants, i.e. each element of the sequence divides the next.