Question
Asked Nov 3, 2019
Suppose that H is a subgroup of G and let G act by conjugation on the set X = {gHg-1 : g ∈ G}. Describe, as precisely as possible, the stabilizer of H under this action.
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Step 1

Given that,

H is a subgroup of G and G act by conjunction on the set

х -{gHe:geG,
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х -{gHe:geG,

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Step 2

The definition of stabilizer given in the following,

Let G be a group which acts on the set X. For x belongs to X, the stabilizer of x in G is the set of elements g belongs to G such that,

g . x = x

Therefore,

stabe (x){geG|gx = x}
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stabe (x){geG|gx = x}

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Step 3

Now assum...

χεΧ
Also, e.x x
and e e stab (x)
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χεΧ Also, e.x x and e e stab (x)

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