Let $G$ be a finite group and $U\subset G$ such that $|U|$ and $|G|$ are relatively prime. Is the stabilizer of $U$ under conjugation action by $G$ trivial?
2026-04-22 05:51:25.1776837085
Finite group G acts on a subset by conjugation
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No. If the group is abelian, the conjugation action is trivial and the stabiliser of any subset of $G$ is the whole group.