Question

Asked Nov 3, 2019

Suppose that *H* is a subgroup of *G* and let *G* act by conjugation on the set *X* = {g*H*g^{-1} : g ∈ *G*}. Describe, as precisely as possible, the stabilizer of *H* under this action.

Step 1

Given that,

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

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,

Step 3

Now assum...

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