[GAP Forum] units of group algebras

[Alexander Konovalov]

Dear Fergal,

if you have a p-group and a field of p elements, then
NormalizedUnitGroup and PcNormalizedUnitGroup from the 
LAGUNA package will help:

gap> KG := GroupRing( GF( 2 ), DihedralGroup( 16 ) );
<algebra-with-one over GF(2), with 4 generators>
gap> V := NormalizedUnitGroup( KG );
<group of size 32768 with 15 generators>
gap> u := GeneratorsOfGroup( V )[4];
(Z(2)^0)*f1+(Z(2)^0)*f2+(Z(2)^0)*f1*f2  
gap> W := PcNormalizedUnitGroup( KG );
<pc group of size 32768 with 15 generators>
gap> w := GeneratorsOfGroup( W )[4];
f4

For other cases I'm afraid that straightforward calculations
will allow to deal only with small examples.

Best wishes,
Alexander
  

On 12 Sep 2013, at 11:58, Fergal Gallagher <Gallagher.Fergal at itsligo.ie> wrote:

> Hi guys,
> 
> I want to check the structure of the unit groups of certain finite group algebras.
> 
> I am new to GAP and have tried the manual but it is very complicated even for the most basic task. ie. find the unit group of F2^2C2xC4 for example.
> 
> Any help?
> 
> Fergal Gallagher
> 
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