Prove that a finite group G is nilpotent if and only if every maximal proper subgroup of
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Prove that a finite group G is nilpotent if and only if every maximal proper subgroup of G is normal. Conclude that every maximal proper subgroup has prime index.
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ANSWER Proof First assume that G is nilpotent We will show that every maximal proper subgroup of G is normal Let H be a maximal proper subgroup of G a...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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