> < ^ Date: Thu, 26 Mar 1998 18:45:18 +0000 (GMT)
> < ^ From: Alexander Hulpke <hulpke@math.colostate.edu >
< ^ Subject: Re: Intersecting Cosets with Subgroups

Dear GAP-Forum,

Matthias Kratzer wrote:

> to compute the intersections of the left cosets of the centre of a
> group G with the G's derived subgroup I tried
> Applied to G=SymmetricGroup(4) these two lines did their job pretty
> good. But why do they fail, when I define G as the cyclic group of
> order 7 ?
> In spite of any result here I only got the following error-message:
> Error, usage: RightCoset( <U> [, <g>] ) in
> RightCoset( arg[1] ) called from
This is an error in the intersection routine. Many thanks for reporting it.

> I think the upper two lines won't work iff
> G is an abelian group iff DerivedSubgroup(G) is trivial and so has
> an empty generator set. Am I right?

I don't understand your double if-and-only-if condition, but the problem is
not with missing generators but with the Centre being the full group:

The problem is in the intersection routine GroupOps.Intersection which does
not treat properly the case of objects which have the same elements as a
group but are not a group. A future fix will contain a correction for this

In your example the Centre of the cyclic group is
the group itself and therefore the one coset contains the same elements as
the group. You can avoid this problem by calling `Elements' as you did.
There is no performance penalty; this is what the correct code will do

Best regards,

Alexander Hulpke

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