MathDB
Permutation Group Of A Set And Conjucate Elements

Source: Miklos Schweitzer 2015,P6

April 8, 2016
group theorysuperior algebracollege contests

Problem Statement

Let GG be the permutation group of a finite set Ω\Omega.Consider S⊂GS\subset G such that 1∈S1\in S and for any x,y∈Ωx,y\in \Omega there exists a unique element σ∈S\sigma \in S such that σ(x)=y\sigma (x)=y.Prove that,if the elements of S∖{1}S \setminus \{1\} are conjugate in GG,then GG is 2−2-transitive on Ω\Omega
Back to ProblemsView on AoPS