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    Our teacher has taught us groups but cant apply his teachings to answers questions from the book.


    Let G be a commutative group. Prove that the set of elements of order 2, together with the identity element, that is H = ( a member of G : A^2 = e), is a subgroup of G

    Take an element g in H which is not the identity. Then it is its own inverse, so every element has an inverse. Take another element h in H. The (gh)(gh)=(gh)(hg) by commutativity, = g(hh)g by associativity = gg = e, so the group is closed. You have an identity, and associativity follows from the fact G is also associative, being a group.
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