DerivedSubgroup( G )
DerivedSubgroup returns the derived subgroup <G>^prime = [ <G>, <G>
] of G.
The derived subgroup of G is the group generated by all commutators [ g, h ] with g, h in <G>.
DerivedSubgroup sets and tests
CommutatorSubgroup (see CommutatorSubgroup) allows you to compute the
commutator group of two subgroups.
gap> s4 := Group( (1,2,3,4), (1,2) ); Group( (1,2,3,4), (1,2) ) gap> DerivedSubgroup( s4 ); Subgroup( Group( (1,2,3,4), (1,2) ), [ (1,3,2), (2,4,3) ] )
Let G be generated by g_1, ..., g_n. Then the default function
GroupOps.DerivedSubgroup returns the normal closure of S under G
where S is the subgroup of G generated by Comm( g_i, g_j ) for 1
leq j < i leq n.
Previous Up Top Next