> < ^ Date: Wed, 25 Mar 1998 12:30:56 +0100 (CET)
> < ^ From: Mathias Kratzer <kratzer@exp-math.uni-essen.de >
> ^ Subject: Intersecting Cosets with Subgroups

Dear GAP-Forum,

to compute the intersections of the left cosets of the centre of a
group G with the G's derived subgroup I tried

gap> Glcs := LeftCosets( G, Centre(G));;
gap> List( Glcs, c -> Intersection( c, DerivedSubgroup(G) ) );

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
Coset( G ) called from
GroupOps.Intersection( G, H ) called from
D.operations.Intersection( I, D ) called from
Intersection( c, DerivedSubgroup( G ) ) called from

I also tried calling

gap> List( Gcls ........, Elements( DerivedSubgroup(G) ) ... );
and because of the fact that this did not yield an error-message,
but the correct result, 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?

Thanks in advance,


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