(a) Let G be a group such that |x| = 2 for every x e. Prove that G is abelian. (b) Let G be an abelian group. Prove that the set of elements of G of finite order is a subgroup of G. (c) Consider the following elements of GL2(R): 1 a = b = - 1 Show that Ja| = 3, |6| = 4, but |ab| = ∞.

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Q: 8. Let G be a finite abelian group. (a) Let d be a positive divisor of |G|. Prove that G has a…

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