# stabilizer

Let $G$ be a group, $X$ a set, and $\cdot:G\times X\longrightarrow X$ a group action. For any subset $S$ of $X$, the of $S$, denoted $\operatorname{Stab}(S)$, is the subgroup

 $\operatorname{Stab}(S):=\{g\in G\mid g\cdot s\in S\text{for all }\ s\in S\}.$

The stabilizer of a single point $x$ in $X$ is often denoted $G_{x}$.

Title stabilizer Stabilizer 2013-03-22 12:12:22 2013-03-22 12:12:22 djao (24) djao (24) 7 djao (24) Definition msc 20M30 msc 16W22 isotropy subgroup