- #1
mathmajor2013
- 26
- 0
Let G be a group, H a normal subgroup, N a normal subgroup, and H intersect N = {e}. Let H x N be the direct product of H and N. Prove that f: HxN->G given by f((h,n))=hn is an isomorphism from HxN to the subgroup HN of G.
Hint: For all h in H and n in N, hn=nh.
Hint: For all h in H and n in N, hn=nh.