Subgroups and Subgroup Series

Some functions for various standard subgroups or series which are only available for p-groups.

Agemo(G, i) : GrpPC, RngIntElt -> GrpPC

Given a p-group G, return the characteristic subgroup of G generated by the elements x^(p^i), x in G, where i is a positive integer.

JenningsSeries(G) : GrpPC -> [GrpPC]

Given a p-group G, return the Jennings series for G. The series is returned as a sequence of subgroups. The Jennings series J_1 triangleright J_2 triangleright ... triangleright J_i ... of a p-group G is defined inductively as follows:

• J_1 = G,
• J_(i + 1) = <(J_i, G), J_k^p>, with k = Ceiling((i + 1)/p), i > 0.

Omega(G, i) : GrpPC, RngIntElt -> GrpPC

Given a p-group G, return the characteristic subgroup of G generated by the elements of order dividing p^i, where i is a positive integer.