(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

(a)Let H and K be subgroups of a group G. Prove that the intersection of xH and yK which are cosets of H and K is either empty or else is a coset of the subgroup H intersect K

(b) Prove that if H and K have finite index in G then the intersection of H and K also has finite index.

2. Relevant equations

3. The attempt at a solution

The intersection of xH and yK is a subgroup of both H and K, then how to continue?

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# A problem from Artin's algebra textbook

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