25.25 AgGroup

AgGroup( D )

AgGroup converts a finite polycyclic group D into an ag group G. G.bijection is bound to isomorphism between G and D.

    gap> S4p := Group( (1,2,3,4), (1,2) );
    Group( (1,2,3,4), (1,2) )
    gap> S4p.name := "S4_PERM";;
    gap> S4a := AgGroup( S4p );
    Group( g1, g2, g3, g4 )
    gap> S4a.name := "S4_AG";;
    gap> L := CompositionSeries( S4a );
    [ S4_AG, Subgroup( S4_AG, [ g2, g3, g4 ] ),
      Subgroup( S4_AG, [ g3, g4 ] ), Subgroup( S4_AG, [ g4 ] ),
      Subgroup( S4_AG, [  ] ) ]
    gap> List( L, x -> Image( S4a.bijection, x ) );
    [ Subgroup( S4_PERM, [ (1,2), (1,3,2), (1,4)(2,3), (1,2)(3,4) ] ),
      Subgroup( S4_PERM, [ (1,3,2), (1,4)(2,3), (1,2)(3,4) ] ),
      Subgroup( S4_PERM, [ (1,4)(2,3), (1,2)(3,4) ] ),
      Subgroup( S4_PERM, [ (1,2)(3,4) ] ), Subgroup( S4_PERM, [  ] ) ] 

Note that the function will not work for finitely presented groups, see AgGroupFpGroup for details.

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