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For a group G, the subset Z(G) = {x Є G|xg = gx, Vg ЄG } is called the center of G. Prove that Z(G) is a subgroup of G.

For a group G, the subset Z(G) = {x Є G|xg = gx, Vg ЄG } is called the center of G. Prove that Z(G) 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
Section4.5: Normal Subgroups
Problem 24E: 24. The center of a group is defined as Prove that is a normal subgroup of .
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For a group G, the subset Z(G) = {x Є G|xg = gx, Vg ЄG } is called the center of G. Prove that Z(G) is a subgroup of G.
Transcribed Image Text:For a group G, the subset Z(G) = {x Є G|xg = gx, Vg ЄG } is called the center of G. Prove that Z(G) is a subgroup of G.
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