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
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