- #1

Bashyboy

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## Homework Statement

Assume that ##H## is a normal subgroup of ##G##, ##\mathcal{K}## is a conjugacy class of ##G## contained in ##H##, and ##x \in \mathcal{K}##. Prove that ##\mathcal{K}## is a union of ##k## conjugacy classes of equal size in ##H##, where ##k = |G : HC_G(x)|##

## Homework Equations

## The Attempt at a Solution

Okay. I need a little help interpreting this problem. Is the problem asking me to show that ##\mathcal{K} = \bigcup_{i \in I } \mathcal{H}_i## with ##|I| = k##, where the ##\mathcal{H}_i## are the conjugacy classes formed by letting ##H## act on itself by conjugation, or are the ##\mathcal{H}_i## the conjugacy classes formed by letting ##G## act on itself by conjugation that are contained in ##H##?

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