Let H,K,N be nontrivial normal subgroups of a group G and suppose G = H X K.

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Let H,K,N be nontrivial normal subgroups of a group G and suppose G = H X K. Prove that N is in the center of G or N intersects one of H,K nontrivially. Give examples to show that both possibilities can actually occur when G is nonabelian.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 13, 2023 03:08 AM

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Let H,K,N be nontrivial normal subgroups of a group G and suppose G = H X K.

Question:

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ANSWER First let us prove that N is in the center of G or intersects one of HK nontrivially Since G ...View the full answer

Algebra Graduate Texts In Mathematics 73

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