WhiteheadPermGroup( X )
This function first calls WhiteheadGroupTable
, see
refWhiteheadGroupTable. These lists are then converted to
permutations, producing a permutation group which is effectively a
regular representation of the group. A field .WhiteheadPermGroup
is
added to X.actorSquare
and a field .genpos
is added to
D = X.derivations. The latter is a list of the positions in
D.genimageList
corresponding to the chosen generating elements. The
group is given the name WG(<name of X>)
.
For an example, we return to the crossed module XSC = [c3->s3]
obtained from the cat1-group SC
in section refCat1Select which
has Whitehead group and automorphism group isomorphic to s3
.
gap> WG := WhiteheadPermGroup( XSC ); WG([c3->s3]) gap> XSC.derivations.genpos; [ 2, 4 ] gap> Elements( WG ); [ (), (1,2,3)(4,6,5), (1,3,2)(4,5,6), (1,4)(2,5)(3,6), (1,5)(2,6)(3,4), (1,6)(2,4)(3,5) ]
GAP 3.4.4