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

[Murthy Sandeep]

OK, if A was the product of D8 and C2 (i.e. if A := DirectProduct( DihedralGroup( 8 ), CyclicGroup( 2 ) ))
then the output of AsList( A ); is

gap> AsList( A );
[ <identity> of ..., f1, f2, f3, f4, f1*f2, f1*f3, f1*f4, f2*f3, f2*f4, f3*f4, f1*f2*f3, f1*f2*f4, f1*f3*f4, f2*f3*f4,
  f1*f2*f3*f4 ]

which is not that given in the earlier message, which appear to be maps.

Sandeep

> On 20 Apr 2015, at 11:52, Mike Newman <newman2603 at gmail.com> wrote:
> 
> Hi,
> 
> The group A is C2 x D8 not D16.
> 
> Regards,
> 
> Mike Newman
> 
> 
> 
> 
> 
> 
> On 20/04/2015, at 8:24 PM, Murthy Sandeep <sandeep at sandeepmurthy.is> wrote:
> 
>> 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
>>> ] ]
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