- #1
StudentR
- 7
- 0
GroupTheory - Isomorphisms
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
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