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

If G is an abelian group, show that H = { a in G | a^2=1} is a subgroup of G.

Give an example where H is not a subgroup.

3. The attempt at a solution

For showing H is a subgroup of G, hh' in G and h^-1 in G.

(a^2)(a^2) in G also a = a^-1 in G so H is a subgroup of G.. right?

counterexample is Z+_(4) = {0,1,2,3,4}.. right?

Thanks

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# Give an example where H is not a subgroup.

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