Definition 4.24: Let G be a group, and let Ω be the set of subgroups of G. Let G act on Ω by conjugation and let H ∈ Ω. For this action, the stabilizer of H in G is called the normalizer of H in G and is denoted by N_G(H). By definition, the normalizer of a subgroup H consists of those elements g ∈ G such that gHg^{−1} =

Definition 4.24: Let G be a group, and let Ω be the set of subgroups of G. Let G act on Ω by conjugation and let H ∈ Ω. For this action, the stabilizer of H in G is called the normalizer of H in G and is denoted by N_G(H). By definition, the normalizer of a subgroup H consists of those elements g ∈ G such that gHg^{−1} =

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 31E: Exercises 31. Let be a group with its center: . Prove that if is the only element of order in ,...

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Exercises 31. Let be a group with its center: . Prove that if is the only element of order in , then .
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