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2. Let G be a group, and let A be a non-empty subset of G. Define Ca(A) = {g G | gag¹ = a for all a € A}. Prove that CG(A) is a subgroup of G.

2. Let G be a group, and let A be a non-empty subset of G. Define Ca(A) = {g G | gag¹ = a for all a € A}. Prove that CG(A) is a subgroup of G.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.6: Quotient Groups
Problem 18E: 18. If is a subgroup of the group such that for all left cosets and of in, prove that is...
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= a 2. Let G be a group, and let A be a non-empty subset of G. Define CG(A) = {g €G | gag ¹ for all a € A}. Prove that Co(A) is a subgroup of G.
Transcribed Image Text:= a 2. Let G be a group, and let A be a non-empty subset of G. Define CG(A) = {g €G | gag ¹ for all a € A}. Prove that Co(A) is a subgroup of G.
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