Answer to Question #309091 in Abstract Algebra for Chinmoy kumar Bera

Abstract Algebra

Question #309091

Let G be a finite group.let S={g€G|g^5=e}, where e is identity element of G.show that |S| is odd.

Expert's answer

Since "g^{-1}=g" only for "g=e" , all "g\\in S" are divided into pairs except "g=e" . Then the size of S is 2n+1, where n is number of pairs.

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