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Hey i'm stuck on these 2 questions, was wondering if anyone could assist me:

Let G be a nontrivial group.

1) Show that if any nontrivial subgroup of G coincides with G then G is isomorphic to C_p, where p is prime. (C_p is the cyclic group of order p!)

2) Show that if any nontrivial subgroup of G is isomorphic to G then G is isomorphic to Z or C_p, where p is prime. (Z is the set of integers, C_p is the cyclic group of order p!)

Thanks, help would be much appreciated

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# Homework Help: Group Theory - Isomorphism question

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