Cyclic quotients of transitive groups

[摘要] Let A be a transitive subgroup of S-n. 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. (C) 2000 Academic Press.

[发布日期] 2000-12-15

[关键词] cyclic quotients;transitive groups;permutation groups;coverings of curves;primitive groups;point stabilizer;Galois theory;field extensions;procyclic fields;extension of constants