# Abstract Algebra-Isomorphism

by TheForumLord
Tags: abstract, algebraisomorphism
 P: 108 1. The problem statement, all variables and given/known data Let A,B be normal sub-groups of a group G. G=AB. Prove that: G/AnB is isomorphic to G/A*G/B Have no idea how to start...Maybe the second isom. theorem can help us... TNX! 2. Relevant equations 3. The attempt at a solution
 P: 352 Use the internal characterization of direct products of groups: if $$G$$ has two normal subgroups $$H, K$$ such that $$HK = G$$ and $$H \cap K = 1$$, then $$G \cong H \times K$$. Also, the third isomorphism theorem may help you (if $$K \subset H$$ are both normal subgroups of $$G$$, then $$G/H \cong (G/K)/(H/K)$$).
 P: 108 Sry but I rly can't figure out the Latex text (I see it in black, and it's realy not clear)... If I understand what you're saying, then we don't have the right conditions to use "internal characterization of direct products of groups"... A,B are normal sub-groups of G and AB=G but who said AnB={1}? The isomorphism you've put afterwards is relevant only when G=A*B and it isn't the case/// Am I wrong? TNx
P: 108

## Abstract Algebra-Isomorphism

I've managed to prove it...TNX a lot anyway...

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