CommutatorSubgroup( G, H )
Let G and H be groups with a common parent group.
CommutatorSubgroup returns the commutator subgroup [ G, H ].
The commutator subgroup of G and H is the group generated by all commutators [ g, h ] with g in <G> and h in <H>.
gap> s4 := Group( (1,2,3,4), (1,2) ); Group( (1,2,3,4), (1,2) ) gap> d8 := Group( (1,2,3,4), (1,2)(3,4) ); Group( (1,2,3,4), (1,2)(3,4) ) gap> CommutatorSubgroup( s4, AsSubgroup( s4, d8 ) ); Subgroup( Group( (1,2,3,4), (1,2) ), [ (1,3)(2,4), (1,3,2) ] )
Let G be generated by g_1, ..., g_n and H be generated by h_1,
..., h_m. 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 (see Hup67). The
GroupOps.CommutatorSubgroup returns the normal closure
of S under the closure of G and H.
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