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-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.
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