Let G be a group. (consider the following parts that go together): (1) Prove that (a-1ba)n...

Let G be a group. (consider the following parts that go together):

(1) Prove that (a^-1ba)ⁿ = a^-1bⁿa for any a,b in G, and any integer n.

(2) Prove that |xax^-1| = |a| for any a, x in G.

(3) Prove: If a is the only element of order two in G, then a lies in Z(G) where Z is the center of the group, G.

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Colby Messinger answered 1 year ago

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