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).
GAP 3.4.4