\documentclass[12pt]article \usepackageamsmath, amssymb, amsthm \usepackageenumitem \usepackagetikz-cd \usepackagehyperref
\subsection*Exercise 6 Let $G$ act on $A$. Define $a\sim b$ if $b = g\cdot a$ for some $g\in G$. Show this is an equivalence relation. dummit+and+foote+solutions+chapter+4+overleaf+full
\beginproof The group $G$ acts on itself by conjugation. The orbit of an element $x$ under this action is its conjugacy class, denoted $\mathcalO_x$ or $\textCl(x)$. The stabilizer of $x$ is the centralizer $C_G(x) = \g \in G \mid gxg^-1 = x\$. dummit+and+foote+solutions+chapter+4+overleaf+full