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Show that Z2 is the only group that has exactly two conjugacy classes

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 34E

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Question

Show that Z₂ is the only group that has exactly two conjugacy classes

Expert Solution

Step 1

Here we know that, $ℤ_{2} = \{0, 1\}$ .

To show that $ℤ_{2}$ is the only group that has exactly two conjugacy classes.

Conjugacy class of an element $a \in G$ contains all conjugates of $a .$

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