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February 15, 2022 10:35 pm 30 pts
Q.37 Let G be a finite group of order at least two and let e denote the identity element of G. Let d: G~ G be a bijective group homomorphism that satisfies the following two conditions: ) Ifog) =g for some g EG, then g =e, ute nolo Gi) (go o)) = g for all g E G. Then which of the following is/are correct? (A) For each g E G, there exists h E G such that ha(h) = g. (B) There exists x E G such that xo(X) # e. (C) The map a satisfies o(x) = xl for every x E G. (D) The order of the group G is an odd number.
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• Navdeep goyal 1
check no G contain 2 order element so order of G is odd C,D