IsCentral( G, U )
true if the group G centralizes the group U and
A group G centralizes a group U if and only if for all g in <G> and for all u in <U> the equation g* u = u* g holds. Note that U need not to be a subgroup of G but they must have a common parent group.
IsCentral sets and tests
U.isCentral if G is the parent
group of U.
gap> s4 := Group( (1,2,3,4), (1,2) );; gap> d8 := Subgroup( s4, [ (1,2,3,4), (1,2)(3,4) ] );; gap> c2 := Subgroup( s4, [ (1,3)(2,4) ] );; gap> IsCentral( s4, c2 ); false gap> IsCentral( d8, c2 ); true
The default function
GroupOps.IsCentral tests whether G centralizes
U by testing whether the generators of G commutes with the generators
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