Recall that the center of a group G is the set {x € G | xg = gx for all g e G}. Prove that he center of G is a normal subgroup of G.
Recall that the center of a group G is the set {x € G | xg = gx for all g e G}. Prove that he center of G is a normal subgroup of G.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.5: Normal Subgroups
Problem 24E: 24. The center of a group is defined as
Prove that is a normal subgroup of .
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the center of G is a normal subgroup of G.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d81790d-312c-4d7a-a8ef-b198a0eb3a23%2F019bd995-9c07-412c-81b2-e916f908884b%2Fyifmn3p_processed.png&w=3840&q=75)
Transcribed Image Text:Recall that the center of a group G is the set {x € G | xg = gx for all g e G}. Prove that
the center of G is a normal subgroup of G.
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