The number of centralizers of a finite group. Let G be a finite group. A subgroup of G may be the centralizer of an element of G. Count the number of such subgroups of G, and call the answer #Cent (G) (a) Show that G is abelian if and only if #Cent(G) = 1. %3D
The number of centralizers of a finite group. Let G be a finite group. A subgroup of G may be the centralizer of an element of G. Count the number of such subgroups of G, and call the answer #Cent (G) (a) Show that G is abelian if and only if #Cent(G) = 1. %3D
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.4: Cosets Of A Subgroup
Problem 14E: Let H be a subgroup of a group G. Prove that gHg1 is a subgroup of G for any gG.We say that gHg1 is...
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