ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 15 Dec 2010 09:35:17 +0100intersection of subgroupshttps://ask.sagemath.org/question/7520/intersection-of-subgroups/I have a group and I'd like to compute the intersection of 2 certain subgroups.
How can I compute the intersection in Sage?
Sun, 12 Dec 2010 11:11:21 +0100https://ask.sagemath.org/question/7520/intersection-of-subgroups/Answer by niles for <p>I have a group and I'd like to compute the intersection of 2 certain subgroups.
How can I compute the intersection in Sage?</p>
https://ask.sagemath.org/question/7520/intersection-of-subgroups/?answer=11862#post-id-11862I 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
()
(1,2)(3,4)
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.Wed, 15 Dec 2010 09:35:17 +0100https://ask.sagemath.org/question/7520/intersection-of-subgroups/?answer=11862#post-id-11862