A classification of certain maximal subgroups of symmetric groups

Authors

Benjamin Newton
Bret Benesh, College of Saint Benedict/Saint John's UniversityFollow

Document Type

Article

Publication Date

10-2006

Disciplines

Algebra | Mathematics

Abstract

Problem 12.82 of the Kourovka Notebook asks for all ordered pairs (n,m) such that the symmetric group Sn embeds in Sm as a maximal subgroup. One family of such pairs is obtained when m=n+1. Kalužnin and Klin [L.A. Kalužnin, M.H. Klin, Certain maximal subgroups of symmetric and alternating groups, Math. Sb. 87 (1972) 91–121] and Halberstadt [E. Halberstadt, On certain maximal subgroups of symmetric or alternating groups, Math. Z. 151 (1976) 117–125] provided an additional infinite family. This paper answers the Kourovka question by producing a third infinite family of ordered pairs and showing that no other pairs exist.

Comments

DOI: 10.1016/j.jalgebra.2005.12.020

Copyright © 2005 Elsevier Inc. All rights reserved. Terms and Conditions

Recommended Citation

Newton B, Benesh B. 2006. A classification of certain maximal subgroups of symmetric groups. Journal of Algebra 304(2): 1108-1113.