57.8 AutomorphismsPGroup

AutomorphismsPGroup( G )
AutomorphismsPGroup( G, output-level)

Let G be a p-group. Then AutomorphismsPGroup returns a generating set for the automorphism group of G. Each generator is described by its action on each of the generators of G. The runtime-information generated by the ANU pq is displayed at output-level, which must be a integer from 0 to 3.

We illustrate the function using the p-group considered above.

    gap> Auts := AutomorphismsPGroup (G);
    [ GroupHomomorphismByImages( Group( G.1, G.2, G.3, G.4, G.5,
        G.6 ), Group( G.1, G.2, G.3, G.4, G.5, G.6 ),
        [ G.1, G.2, G.3, G.4, G.5, G.6 ],
        [ G.1, G.2*G.5^2, G.3, G.4, G.5, G.6 ] ),
      GroupHomomorphismByImages( Group( G.1, G.2, G.3, G.4, G.5,
        G.6 ), Group( G.1, G.2, G.3, G.4, G.5, G.6 ),
        [ G.1, G.2, G.3, G.4, G.5, G.6 ],
        [ G.1, G.2*G.3, G.3, G.4, G.5, G.6 ] ),
      GroupHomomorphismByImages( Group( G.1, G.2, G.3, G.4, G.5,
        G.6 ), Group( G.1, G.2, G.3, G.4, G.5, G.6 ),
        [ G.1, G.2, G.3, G.4, G.5, G.6 ], [ G.1*G.3^2, G.2, G.3*G.5, G.4,
          G.5, G.6 ] ), GroupHomomorphismByImages( Group( G.1, G.2, G.3,
        G.4, G.5, G.6 ), Group( G.1, G.2, G.3, G.4, G.5, G.6 ),
        [ G.1, G.2, G.3, G.4, G.5, G.6 ],
        [ G.1*G.6, G.2*G.6, G.3, G.4, G.5, G.6 ] ),
      GroupHomomorphismByImages( Group( G.1, G.2, G.3, G.4, G.5,
        G.6 ), Group( G.1, G.2, G.3, G.4, G.5, G.6 ),
        [ G.1, G.2, G.3, G.4, G.5, G.6 ], [ G.1*G.5^2, G.2*G.5, G.3, G.4,
          G.5, G.6 ] ), GroupHomomorphismByImages( Group( G.1, G.2, G.3,
        G.4, G.5, G.6 ), Group( G.1, G.2, G.3, G.4, G.5, G.6 ),
        [ G.1, G.2, G.3, G.4, G.5, G.6 ], [ G.1*G.6^2, G.2*G.6, G.3, G.4,
          G.5, G.6 ] ), GroupHomomorphismByImages( Group( G.1, G.2, G.3,
        G.4, G.5, G.6 ), Group( G.1, G.2, G.3, G.4, G.5, G.6 ),
        [ G.1, G.2, G.3, G.4, G.5, G.6 ],
        [ G.1*G.4, G.2*G.4*G.6, G.3, G.4*G.6, G.5, G.6 ] ),
      GroupHomomorphismByImages( Group( G.1, G.2, G.3, G.4, G.5,
        G.6 ), Group( G.1, G.2, G.3, G.4, G.5, G.6 ),
        [ G.1, G.2, G.3, G.4, G.5, G.6 ],
        [ G.1^2*G.3^2, G.2^2*G.3, G.3*G.5, G.4^2, G.5^2, G.6^2 ] ) ] 

This function requires the package "anupq" (see RequirePackage).

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GAP 3.4.4
April 1997