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I need help here: Suppose that G is a group in which every non-identity element has order two. Show that G is commutative.
Also, Consider Zn = {0,1,....,n-1}
a. show that an element k is a generator of Zn if and only if k and n are relatively prime.
b. Is every subgroup of Zn cyclic? If so, give a proof. If not, provide an example.
Also, Consider Zn = {0,1,....,n-1}
a. show that an element k is a generator of Zn if and only if k and n are relatively prime.
b. Is every subgroup of Zn cyclic? If so, give a proof. If not, provide an example.