Let H, K be normal subgroups of a group G such that G = H X K.
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Let H, K be normal subgroups of a group G such that G = H X K.
(a) If N is a normal subgroup of H, then N is normal in G (compare Exercise 1.5.10).
(b) If G satisfies the ACC or DCC on normal subgroups, then so do H and K.
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ANSWER a To show that N is normal in G we need to show that for any g hk in G where h H and k K we h...View the full answer
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Related Book For 
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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