Suppose \(G\) is a group acting transitively on a finite set \(S\), \(|S|\geq 2\). Prove that there exists an element \(\sigma \in G\) such that \(\sigma (s)\ne s\), for all \(s\in S\).
Question
Math 6310 • Algebra
Fall 2012 • Question 1
Question
Fall 2012 • Question 1
Suppose \(G\) is a group acting transitively on a finite set \(S\), \(|S|\geq 2\). Prove that there exists an element \(\sigma \in G\) such that \(\sigma (s)\ne s\), for all \(s\in S\).