MathDB

6

Part of 2015 Miklos Schweitzer

Problems(1)

Permutation Group Of A Set And Conjucate Elements

Source: Miklos Schweitzer 2015,P6

4/8/2016
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
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