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} =
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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} = H. In other words, N_G(H) = { g ∈ G such that gHg^{−1} =H }.

Transcribed Image Text:Let G be a group, and let H < G. Recall Definition 4.24 of NG(H), the
normalizer of H in G. Show that
Ng(H) = {x E G| xHx¯
¯1 = H} = {x € G | xH = Hx}.
Expert Solution

Step 1
We prove our claim by using definition of NG(H).
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