... journal of combinatorics 13 (2006), #N16 2On the Proof of a Theorem of P´alfyEdward DobsonDepartment of Mathematics and StatisticsMississippi State UniversityPO Drawer MAMississippi State, ... = 1, then y is conjugate to x in x, y.Proof. As x and y are abelian, and a transitive abelian subgroup is regular [3,Theorem 4. 2A (v)], we have that fixx(B) and fixy(B) have ... solvable, and in that case any two Hall π-subgroups of G are conjugate in G.Definition 2 Let G be a transitive permutation group of degree mk that admits a com-plete block system B of m blocks of...