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. Let G be a group and a e G. An element be G is called a conjugate of a if there exists an element a € G such that b = xax-. Show that if b is a conjugate of a then o(b) = o(a).

. Let G be a group and a e G. An element be G is called a conjugate of a if there exists an element a € G such that b = xax-. Show that if b is a conjugate of a then o(b) = o(a).

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.4: Cyclic Groups
Problem 31E: Exercises 31. Let be a group with its center: . Prove that if is the only element of order in ,...
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Let G be a group and a E G. An element b eG is called a conjugate of a if there exists an element r E G such that b = xax. Show that if b is a conjugate of a then o(b) = o(a).
Transcribed Image Text:Let G be a group and a E G. An element b eG is called a conjugate of a if there exists an element r E G such that b = xax. Show that if b is a conjugate of a then o(b) = o(a).
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