Question 5: Let G be a group, o an automorphism of G, N a normal subgroup of G. Prove that (N) is a normal subgroup of G.
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- Let H and K be subgroups of a group G and K a subgroup of H. If the order of G is 24 and the order of K is 3, what are all the possible orders of H?Let G be an abelian group of order 2n, where n is odd. Use Lagranges Theorem to prove that G contains exactly one element of order 2.5. For any subgroup of the group , let denote the product as defined in Definition 4.10. Prove that corollary 4.19: