[GAP Forum] what does Group([ f1 ]), Group ([ f2 ]), mean.

[Murthy Sandeep]

f1, f2, f3, f4 are labels for the generators of D16:

gap> GeneratorsOfGroup( DihedralGroup( 16 ) );
[ f1, f2, f3, f4 ]

and the generators of Aut( D16) are described in
terms of these:

gap> GeneratorsOfGroup( AutomorphismGroup( DihedralGroup( 16 ) ) );
[ Pcgs([ f1, f2, f3, f4 ]) -> [ f1*f2, f2, f3, f4 ], Pcgs([ f1, f2, f3, f4 ]) -> [ f1*f3*f4, f2, f3, f4 ],
  Pcgs([ f1, f2, f3, f4 ]) -> [ f1, f2*f3*f4, f3*f4, f4 ], Pcgs([ f1, f2, f3, f4 ]) -> [ f1*f4, f2, f3, f4 ],
  Pcgs([ f1, f2, f3, f4 ]) -> [ f1, f2*f4, f3, f4 ] ]

If x1,…,x_n are elements of a group G then Group( [x1,…,x_n] ) is the subgroup generated
by these elements.

Sandeep

> On 20 Apr 2015, at 11:10, abdulhakeem alayiwola <lovepgroups at gmail.com> wrote:
> 
> when Gap list groups as shown below what does f1, f2, f3 and the rest stand
> for...
> gap> StructureDescription(A);
> "C2 x D8"
> 
> You can also list the automorphisms explicitly:
> 
> gap> AsList(A);
> [ [ f1*f3, f2*f4 ] -> [ f1*f3, f2*f4 ], [ f1*f3, f2*f4 ] -> [ f1, f2*f4 ],
>  [ f1*f3, f2*f4 ] -> [ f1*f4, f2 ], [ f1*f3, f2*f4 ] -> [ f1*f3*f4, f2 ],
>  [ f1*f3, f2*f4 ] -> [ f1*f3*f4, f2*f3*f4 ], [ f1*f3, f2*f4 ] -> [ f1*f4,
> f2*f3 ],
>  [ f1*f3, f2*f4 ] -> [ f1, f2*f3*f4 ], [ f1*f3, f2*f4 ] -> [ f1*f3, f2*f3
> ],
>  [ f1*f3, f2*f4 ] -> [ f1*f3, f2 ], [ f1*f3, f2*f4 ] -> [ f1, f2 ],
>  [ f1*f3, f2*f4 ] -> [ f1*f4, f2*f4 ], [ f1*f3, f2*f4 ] -> [ f1*f3*f4,
> f2*f4 ],
>  [ f1*f3, f2*f4 ] -> [ f1*f3*f4, f2*f3 ], [ f1*f3, f2*f4 ] -> [ f1*f4,
> f2*f3*f4 ],
>  [ f1*f3, f2*f4 ] -> [ f1, f2*f3 ], [ f1*f3, f2*f4 ] -> [ f1*f3, f2*f3*f4
> ] ]
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum