Dear Forum, If FG is the group algebra of the Dihedral group G of order 6 over the finite field with 9(=3^2) elements, then how can the normalized unit group of FG be obtained. When I take the field with 3 elements, then I am able to get the elements, but if I take the field with 9 elements then what should be the approach.
g:=DihedralGroup(6);; f:=GF(3);; fg:=GroupRing(f,g);; e:=Identity(fg);; m:=MinimalGeneratingSet(g);; l:=List(m,x-> x^Embedding(g,fg));; u:=Units(fg);; s:=Filtered(u, x-> Augmentation(x) = (Z(3)^(0)) );; v:=AsGroup(s);; Print(v); This was the approach I used for group algebra of smaller order, but it didn't work anymore when I increased the size of the field. Moreover, if I take DIhedral group of order 10 over Filed with 5 elements, then again I am facing the same problem. Any suggestions will be highly appreciated. -- *Regards* *Surinder Kaur* *Research scholar * *Department of Mathematics * *IIT Ropar* _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
