NormalClosure( S, U )
Let S and U be groups with a common parent group G. Then
NormalClosure
returns the normal closure of U under S as a subgroup
of G.
The normal closure N of a group U under the action of a group S is the smallest subgroup in G that contains U and is invariant under conjugation by elements of S. Note that N is independent of G.
gap> s4 := Group( (1,2,3,4), (1,2) ); Group( (1,2,3,4), (1,2) ) gap> s4.name := "s4";; gap> d8 := Subgroup( s4, [ (1,2,3,4), (1,2)(3,4) ] ); Subgroup( s4, [ (1,2,3,4), (1,2)(3,4) ] ) gap> NormalClosure( s4, d8 ); Subgroup( s4, [ (1,2,3,4), (1,2)(3,4), (1,3,4,2) ] ) gap> last = s4; true
GAP 3.4.4