# 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?

intersection of subgroups

add a comment

0

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
()
(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.

Asked: **
2010-12-12 04:11:21 -0500
**

Seen: **346 times**

Last updated: **Dec 15 '10**

Solving two-variable equations mod p

Check whether a modular subgroup is congruence from its generators

Action of lattice automorphism group on discriminant group

Working with multiplicative groups

Orbits on group actions acting on sets

PermutationGroupMorphism_im_gens

Iterator for conjugacy classes of Sn

morphism between permutation group and matrix group

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.