A Comment on a Necessary and Sufficient Condition for Transitive Permutation Group by P.J.Cameron

P.J. Cameron had mentioned that "It can be shown that a permutation group is transitive if and only if its centralizer in the symmetric group is semiregular, and vice versa (Wielandt, page 9)."1] The latter is true, i.e. G≤S_Ω is semiregular(?)Cs_Ω(G) is transitive. cf. 2] But in the former statement fails, i.e. Cs_Ω(G) is semiregular(?)G≤S_Ω is transitive. In this note we give a series of the