Dear Dong, Let me second Alexander's explanation. To define a ring, you must supply gap with elements that may be added and multiplied. A simple way to construct ring elements is by converting the permutations to permutation matrices. The short code
gap> GroupRing( GF(2), SymmetricGroup(3) );
could have been written as gap> regularactiongens := GeneratorsOfGroup(Action(SymmetricGroup(3),SymmetricGroup(3),OnRight)); [ (1,3,5)(2,4,6), (1,6)(2,5)(3,4) ] gap> Algebra(GF(2), List(regularactiongens,g->PermutationMat(g,6,GF(2)))); <algebra over GF(2), with 2 generators> This has the disadvantage that GAP does not know that you constructed a group ring (and therefore does not know that there is an augmentation ideal, etc.) -- Laurent Bartholdi \ laurent.bartholdi<at>gmail<dot>com EPFL SB SMA IMB MAD \ Téléphone: +41 21-6935458 Station 8 \ Secrétaire: +41 21-6935471 CH-1015 Lausanne, Switzerland \ Fax: +41 21-6930339 _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
