Let G be a group and the center of G is defined as Z(G) = {x E G | xg = gx for all g E G} We already showed that the center Z(G) is a subgroup of G. Let H be a subgroup of G Prove that the set HZ(G) = {hz | h E H, z E Z(G)}.

Let G be a group and the center of G is defined as Z(G) = {x E G | xg = gx for all g E G} We already showed that the center Z(G) is a subgroup of G. Let H be a subgroup of G Prove that the set HZ(G) = {hz | h E H, z E Z(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 39E

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Let G be a group and the center of G is defined as Z(G) = {x E G | xg = gx for all gE G}
We already showed that the center Z(G) is a subgroup of G.
Let H be a subgroup of G
Prove that the set HZ(G) = {hz | h E H, Z E Z(G)}.

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