Let A be a transitive subgroup of Sn. We show that the largest cyclic quotient of A has order at most n. This can be interpreted as an equivalent result about extensions of constants in the Galois closure of a covering of curves over a finite field. We also prove that the point ...
If Γ is a string C-group which is isomorphic to a transitive subgroup of the symmetric groupSn(other thanSnand the alternating groupAn), then the rank of Γ is at mostn/2+1, with finitely many exceptions (which are classified). It is conjectured that only the symmetric group has to ...