Answer to Question #188091 in Abstract Algebra for Renu

Question

Use the Fundamental Theorem of Homomorphism for Groups to prove the following theorem, which is called the Zassenhaus (Butterfly) Lemma:

Let H and K be subgroups of a group G and H′ and K′ be normal subgroups of H

and K, respectively. Then

i) H′(H ∩ K′) H′(H ∩ K)

ii) K′(H′∩ K) K′(H ∩ K)

Answer 1

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