[GAP Forum] Normalized unit group of group algebra FD6

[Surinder Kaur]

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*