[GAP Forum] speed of Core vs IsNormal

[Alexander Hulpke]

Dear Forum,

On Jan 21, 2011, at 9:11 PM, William DeMeo wrote:


> I apologize if this is a dumb question, but I'm trying to speed up a
> program that is searching for certain groups. In the examples I'm
> looking for, I have a subgroup H of a group G and I need to test
> (among other things) whether it is core-free.  I was wondering if
> someone could tell me whether it would speed things up greatly if I
> first tested to see if the subgroup itself is normal.

It will do a minuscule speedup, but might not be worth unless you have tons of normal subgroups. Basically Core calculates the images of H under the generators of G and tests whether these are new subgroups by testing whether elements are in. IsNormal maps the generators of H under the generators of G and tests whether they still lie in H. This will be a bit faster.

However, since you really care about Core=1 I think that might be a better way to eliminate cases. For example you could try to calculate the minimal normal subgroups and test whether they are contained in. Or in your algorithm collect the (different) wrong cores and before testing normality or the core check whether any of them is a subset of H.

Best regards,

   Alexander Hulpke




-- Colorado State University, Department of Mathematics,
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