P.S. This computation now works too in GAP 4.6.3 and Image(phi2,b)^2 returns an identity matrix. Thanks for reporting this bug!
Best wishes, Alexander On 10 Dec 2012, at 22:04, Neha Wadhwani <nehamakhij...@gmail.com> wrote: > Hi > > I am not able to understand if the following is actually a well defined > homomorphism! > > *G:=DihedralGroup(20);* > <pc group of size 20 with 3 generators> > > *b:=G.1*G.2;* > f1*f2 > > *b^2;* > <identity> of ... > > *phi:=IrreducibleRepresentations(G,GF(8));* > [ Pcgs([ f1, f2, f3 ]) -> [ [ [ Z(2)^0 ] ], [ [ Z(2)^0 ] ], [ [ Z(2)^0 ] ] > ], > Pcgs([ f1, f2, f3 ]) -> > [ [ [ Z(2)^0, 0*Z(2), Z(2^3), Z(2)^0 ], [ 0*Z(2), Z(2)^0, Z(2^3)^6, > Z(2^3)^3 ], [ 0*Z(2), 0*Z(2), Z(2^3), Z(2^3)^3 ], > [ 0*Z(2), 0*Z(2), Z(2^3)^2, Z(2)^0 ] ], > [ [ Z(2^3)^6, Z(2^3)^5, Z(2^3)^6, Z(2^3) ], > [ Z(2^3)^4, Z(2^3), Z(2)^0, Z(2^3)^5 ], > [ Z(2^3)^2, Z(2^3)^6, Z(2^3)^3, Z(2^3)^4 ], > [ Z(2^3)^5, Z(2)^0, Z(2^3)^3, Z(2^3)^6 ] ], > [ [ Z(2^3)^2, Z(2^3)^4, Z(2^3), 0*Z(2) ], > [ Z(2^3)^3, Z(2^3), 0*Z(2), Z(2^3) ], > [ Z(2^3), Z(2^3), Z(2^3)^3, Z(2^3)^5 ], > [ Z(2)^0, 0*Z(2), Z(2^3)^4, Z(2^3)^2 ] ] ] ] > > *phi2:=phi[2];;* > * > * > *Image(phi2,b)^2;* > [ [ Z(2^3)^6, Z(2^3)^3, 0*Z(2), 0*Z(2) ], > [ Z(2^3)^2, Z(2^3)^4, 0*Z(2), 0*Z(2) ], > [ Z(2^3)^4, Z(2^3)^3, Z(2^3), Z(2^3)^6 ], > [ Z(2^3)^2, Z(2^3)^6, Z(2^3)^5, Z(2^3)^5 ] ] > *which is not an identity matrix..* > * > * > *Please let me know if I am going wrong....* > * > * > *Thanks!* > _______________________________________________ > 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
