If G is a group and g E G, the centralizer of g E G, is the set CG(g) := {a E G : ag =ga} that is, it is the subset of elements of G that commute with the given element g. Prove that CG(g) is a subgroup of G without using the isotropic group Gg ={a E G : a*g =g}
If G is a group and g E G, the centralizer of g E G, is the set CG(g) := {a E G : ag =ga} that is, it is the subset of elements of G that commute with the given element g. Prove that CG(g) is a subgroup of G without using the isotropic group Gg ={a E G : a*g =g}
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.8: Some Results On Finite Abelian Groups (optional)
Problem 16E
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If G is a group and g E G, the centralizer of g E G, is the set CG(g) := {a E G : ag =ga} that is, it is the subset of elements of G that commute with the given element g. Prove that CG(g) is a subgroup of G without using the isotropic group Gg ={a E G : a*g =g}
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