(a) If G is a group, then the center of G is a normal subgroup of G...

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(a) If G is a group, then the center of G is a normal subgroup of G (see Exercise 2.11);
(b) the center of Sn is the identity subgroup for all n > 2.

Exercise 2.11

If His a cyclic subgroup of a group G and His normal in G, then every subgroup of His normal in G

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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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(a) If G is a group, then the center of G is a normal subgroup of G...

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a To show that the center ZG of G is a normal subgroup of G we need to show that gZGg1 ZG for all g ...View the full answer

Algebra Graduate Texts In Mathematics 73

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