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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

description

of "GroupRing" function in the manual. I hope that somebody may tell me

where it

lies.

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

described

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); 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

brk>

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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