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14E-b

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Abstract Algebra: An Introduction

Found in: Page 311

Book edition 3rd

Author(s) Thomas W Hungerford, David Leep

Pages 608 pages

ISBN 9781111569624

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Short Answer

Let N be a normal subgroup of G , $a \in G$ , and C the conjugacy class of a in G .
If $C_{i}$ is any conjugacy class in G , prove that $C_{i} \subseteq N$ or $C_{i} \cap N = Φ$ .

It is proved that, $C_{i} \subseteq N$ or $C_{i} \cap N = Φ$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

It is given that N is a normal subgroup of G , $a \in G$ , C is the conjugacy class of a in G and $C_{i}$ is any conjugacy class in G .

Step 2: Prove the statement

If $C_{i} \cap N = Φ$ , then there is nothing to prove.

If $C_{i} \cap N$ is non-empty, then part (a) implies that $C_{i} \subseteq N$ .

It has been concluded that, $C_{i} \subseteq N$ or $C_{i} \cap N = Φ$ .

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