> < ^ Date: Thu, 13 May 1999 19:39:41 +0300
> < ^ From: Alexander B. Konovalov <alexk@mcs.st-and.ac.uk >
> ^ Subject: Group rings in GAP4

Dear GAP-forum,
1. It was a pleasant surprise for me to discover that in GAP4 group rings
are built-in
without any additional share packages. But I still did nit managed to find
of "GroupRing" function in the manual. I hope that somebody may tell me
where it

2. I have tried to compute the group ring of the dihedral group of order 8.
As you can
see below, the number of its generators depends on whether the group is
as pc-group or permutation group. Whether it is right ?

gap> G:=Group((1,2,3,4),(2,4));
Group([ (1,2,3,4), (2,4) ])
gap> G1:=DihedralGroup(8);
<pc group of size 8 with 3 generators>
gap> F:=GF(2);
gap> FG:=GroupRing(F,G);
<algebra-with-one over GF(2), with 2 generators>  # ??????????
gap> FG1:=GroupRing(F,G1);
<algebra-with-one over GF(2), with 4 generators> # ??????????

3. How can I compute the unit group of the group ring ?
In both cases described above I get the same error:

gap> Units(FG);
Error no method found for operation INV with 1 argument
InverseOp( elm ) called from
Inverse( s ) called from
Quotient( R, one, r ) called from
IsUnit( R, elm ) called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop, you can 'quit;' to quit to outer loop,
or you can return to continue

Hope to hear an advice soon.
Sincerely, Alexander Konovalov

Alexander B. Konovalov,
Algebra & Geometry Chair,
Zaporozhye State University, Ukraine
E-mail: konovalov@member.ams.org

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