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(A) Show that if a2=e for all elements a in a group G, then G must...

(A) Show that if a2=e for all elements a in a group G, then G must be abelian.

(B) Show that if G is a finite group of even order, then there is an a∈G such that a is not the identity and a2=e.

(C) Find all the subgroups of Z3×Z3. Use this information to show that Z3×Z3 is not the same group as Z9.

(Abstract Algebra)

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