Normal structure of the one-point stabilizer of a doubly-transitive permutation group. II-Reference-Cited by-同舟云学术

Normal structure of the one-point stabilizer of a doubly-transitive permutation group. II

Published:1975 Issue:0 Volume:214 Page:43-74
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

O’Nan Michael E.

Abstract

The main result is that the socle of the point stabilizer of a doubly-transitive permutation group is abelian or the direct product of an abelian group and a simple group. Under certain circumstances, it is proved that the lengths of the orbits of a normal subgroup of the one point stabilizer bound the degree of the group. As a corollary, a fixed nonabelian simple group occurs as a factor of the socle of the one point stabilizer of at most finitely many doubly-transitive groups.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1975-214-00/S0002-9947-75-99942-0/S0002-9947-75-99942-0.pdf

Reference11 articles.

1. Transitive Gruppen gerader Ordnung, in denen jede Involution genau einen Punkt festläßt;Bender, Helmut;J. Algebra,1971

2. On finite groups of even order whose 2-Sylow group is a quaternion group;Brauer, Richard;Proc. Nat. Acad. Sci. U.S.A.,1959

3. Solvability of groups of odd order;Feit, Walter;Pacific J. Math.,1963

4. Central elements in core-free groups;Glauberman, George;J. Algebra,1966

5. On the automorphism groups of a finite group having no non-identity normal subgroups of odd order;Glauberman, George;Math. Z.,1966

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Permutation Groups with Few Fixed Points;Geometry — von Staudt’s Point of View;1981

2. On the normal structure of a one-point stabilizer in a doubly transitive permutation group;Journal of the Australian Mathematical Society;1978-03