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intersection of subgroups

asked 2010-12-12 11:11:21 +0200

oren gravatar image

I have a group and I'd like to compute the intersection of 2 certain subgroups. How can I compute the intersection in Sage?

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answered 2010-12-15 09:35:17 +0200

niles gravatar image

I don't think there is an automatic way to do this. If your groups are finite, something like the following might be enough:

sage: G = SymmetricGroup(4)
sage: H = G.subgroup([G([(1,2),(3,4)]),G((1,2))])
sage: K = G.subgroup([G((1,3,2,4))])
sage: for k in K:
    if k in H:
        print k

Using a list comprehension does the same thing as the for loop above; you can feed this directly to the subgroup function to get the corresponding subgroup:

sage: G.subgroup([k for k in K if k in H])
Subgroup of SymmetricGroup(4) generated by [(), (1,2)(3,4)]

If your subgroups are countably infinite and the intersection is finite, then maybe some modified version of this will work. Otherwise you may have to be more clever.

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Asked: 2010-12-12 11:11:21 +0200

Seen: 816 times

Last updated: Dec 15 '10