On Thu, September 11, 2014 6:22 pm, hadi Hooshmand wrote:
> Dear All,
>
> Let $G$ be a group of order 192 and $d$ a positive divisor of it . Is it
> true
> that there exists a subgroup of $G$ with order or index $d$?
>
> Is there any GAP code to check the question by an ordinary computer?
> Does anyone know the answer?
Just enter
gap> check := n->ForAll(AllGroups(n),
> G->ForAll(DivisorsInt(n),
> d->Intersection([d,n/d],
>
> List(ConjugacyClassesSubgroups(G),
>
> cl->Size(Representative(cl))))<>[]));;
gap> check(192);
and have some patience.
Hope this helps,
Stefan Kohl
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