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Prove that if g is a finite group h subset of g that is

Please help with the following problems involving group theory proofs. Provide step by step calculations along with explanations.

a) Prove that if G is a finite group and a is an element of G then for some positive m , a^m is equal to the identity of G. (Use the Pigeon hole principle)

b) Prove that if G is a finite group, H subset of G that is closed with respect to the operation of G, Then every element of H has its inverse in H.

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Algebra: Prove that if g is a finite group h subset of g that is

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Algebra: Prove that if g is a finite group h subset of g that is

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