[GAP Forum] MinimalGeneratingSet

[MCKAY john]

Minimal generating sets for simple groups of order up to 10**6

are in the literature... Try K-C Young, J. Cannon, and
myself.

Young pioneered this in his PhD thesis. Rob Wilson
has been perfecting the technique.


John McKay



On Wed, 1 Jun 2005, Stefan Kohl wrote:

> Dear Forum,
>
> On April 14, Jon Cohen asked:
>
> > I think there is a bug with the MinimalGeneratingSet method (I am
> > running GAP 4.4.4 and have installed the latest bugfix).
> >
> > It does not seem to handle nonsolvable permutation groups:
> >
> > gap> MinimalGeneratingSet(SymmetricGroup(4));
> > [ (2,4,3), (1,4,2,3) ]
> >
> > Is fine, but:
> >
> > gap> MinimalGeneratingSet(SymmetricGroup(5));
> >
> > gives an error. A quick look shows that the grpperm.gi code calls the
> > grppcatr.gi MinimalGeneratingSet method only when the input group is
> > solvable.
>
> In general, getting a `no method found' - message does not indicate
> an error. Such a message can indicate that a particular request
> does not make sense. But it can also just mean that simply no suitable
> method has been implemented so far.
>
> Here the latter is the case.
>
> Efficient methods for computing a minimal generating set are so far
> only known for finite solvable groups and for finitely-generated
> nilpotent groups.
>
> Of course, the case of an arbitrary finite group could in principle be
> treated by just looping over all pairs, triples, 4-tuples, ... of
> generators until one finds some k-tuple which generates.
>
> But the performance of this would be that horrible that nobody has seen
> a benefit in implementing it in GAP so far.
>
> Best wishes,
>
>      Stefan Kohl
>
>
>
>
>
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