73.139 AutomorphismPair

AutomorphismPair( A )

This returns a record pairA containing a permutation group isomorphic to the group A obtained using the OperationHomomorphism function. The record contains A and pairA.auto, P as pairA.perm. Isomorphisms in each direction are saved as pairA.p2a and pairA.a2p.

    gap> ac3 := AutomorphismGroup( c3 );
    Group( GroupHomomorphismByImages( c3, c3, [(1,2,3)], [(1,3,2)] ) )
    gap> pairc3 := AutomorphismPair( ac3 );
    rec(
      auto := Aut(c3),
      perm := PermAut(c3),
      a2p := OperationHomomorphism( Aut(c3), PermAut(c3) ),
      p2a := GroupHomomorphismByImages( PermAut(c3), Aut(c3), [(1,2)], 
        [ GroupHomomorphismByImages( c3, c3, [(1,2,3)], [(1,3,2)] ) ] ),
      isAutomorphismPair := true )
    gap> pc3 := pairc3.perm;
    PermAut(c3)  

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