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 <newman2...@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 <sand...@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 <lovepgro...@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@mail.gap-system.org >>> http://mail.gap-system.org/mailman/listinfo/forum >> >> _______________________________________________ >> Forum mailing list >> Forum@mail.gap-system.org >> http://mail.gap-system.org/mailman/listinfo/forum >
_______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
