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

Suppose H and K are subgroups of G. Prove H intersect K is a subgroup of G.

2. Relevant equations

Suppose G is a group and H is a nonempty subset of G. Then H is a subgroup of G iff a,b ∈ H implies ab^-1 ∈ H.

3. The attempt at a solution

Suppose a and b elements of H intersect K. Since H is a subgroup of G and K is a subgroup G, then ab^-1 is an element of H and ab^-1 is an element of K, this implies ab^-1 is an element of H intersect K, this implies H intersect K is a subgroup of G.

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# Intersection of subgroups is a subgroup

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