73.115 WhiteheadPermGroup

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) ]  

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GAP 3.4.4
April 1997