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Unformatted text preview: R ). (b) Prove that the center of G is trivial. (c) Let x = a b 0 1 and y = c d 0 1 be two elements of G . Assuming that neither is the identity element, prove that x and y are conjugate in G if and only if a = c . 4. Let G be a group, and let a be an element of G . The centralizer of a in G is the set C ( a ) = { g G  ga = ag } . Use the twostep subgroup test to prove that C ( a ) is a subgroup of G . 1...
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 Spring '09
 Math, Algebra

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