Abstract :
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 stabilizer in a finite primitive permutation group always has a faithful orbit.
Keywords :
Transitive groups , cyclic quotients , coverings of curves , primitive groups , Galois theory , field extensions , procyclic fields , extension of constants , Permutation groups , point stabilizer
