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.
So, I'm wondering if I should simply do:
e:=Group([Identity(G)]);
if Core(G,H)=e then
# test other search criteria
...
Or would I do better to test for normality of the subgroup first:
if IsNormal(G,H) and H<>e then
# do nothing
elif Core(G,H)=e then
# test other search criteria
Would the latter speed things up greatly? Is computing Core much more
expensive than first testing IsNormal?
Thanks and, again, I apologize if this is dumb.
-William
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