Let G be a group and a ∈ G. A conjugate of a is any element of the form bab-1 for some b ∈ G. Show that if c = bab-1 is a conjugate of a in G and n is any integer, then cn=banb-1. First prove for n ≥ 0 by induction on n.

Let G be a group and a ∈ G. A conjugate of a is any element of the form bab-1 for some b ∈ G. Show that if c = bab-1 is a conjugate of a in G and n is any integer, then cn=banb-1. First prove for n ≥ 0 by induction on n.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 37E

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Let G be a group and a ∈ G. A conjugate of a is any element of the form bab^-1for some b ∈ G. Show that if c = bab^-1 is a conjugate of a in G and n is any integer, then cⁿ=baⁿb^-1.

First prove for n ≥ 0 by induction on n.

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