25.12 CommutatorSubgroup for Ag Groups

AgGroupOps.CommutatorSubgroup( G, H )

Let g_1, ..., g_n be an canonical generating system for G and h_1, ..., h_m be an canonical generating system for H. The normal closure of the subgroup S generated by Comm( g_i, h_j ) for 1 leq i leq n and 1 leq j leq m under G and H is the commutator subgroup of G and H.

But if G or H is known to be normal in the common parent of G amd H then the subgroup S is returned because if G normalizes H or vice versa then S is already the commutator subgroup (see Gla87).

If <G> = <H> the commutator subgroup is generated by Comm( g_i, g_j ) for 1 leq i < j leq n (see LNS84). Note that AgGroupOps.CommutatorSubgroup checks G.derivedSubgroup in that case.

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