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Dear gap-forum

On Fri, Mar 30, 2001 at 12:53:02PM -0500, Igor Schein wrote:

> On Wed, Mar 28, 2001 at 11:10:33AM +0200, Stefan Kohl wrote:

> > Dear gap-forum,

> >

> > Igor Schein wrote:

> >

> > > I'm far from being sophisticated in group theory and GAP, so please

> > > bear with me. In GAP 4.x I can access database of groups by using

> > > function SmallGroup, e.g. SmallGroup(32,1). What I need is to

> > > find out the number of quadratic residues for, say, the group above.

> > > Is it possible for arbitrary SmallGroup(n,k) as long as the group is

> > > in the database? Going further, I would like to construct a

> > > multiplication table for SmallGroup(32,k). Is it possible in GAP?

> >

> > You can get the number of quadratic residues in the group G

> > by using the function

> >

> > NumQuadRes := G -> Length(Set(List(AsList(G),g->g^2)));

> >

> > You can get a multiplication table of the group G by

> >

> > MultiplicationTable(AsList(G));

Thanks a lot, Stefan, this was very useful.

I have a somewhat related question. There're 51 groups of order 32, and

some of them are very hard to distinguish. For example,

SmallGroup(32,27) and SmallGroup(32,34). Are there standard methods (

preferable ones that can be done in GAP ) to determine whether or not 2

groups like above are isomorphic?Thanks

Igor

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