Published online by Cambridge University Press: 05 July 2011
Abstract
We discuss the completion of the classification of maximal subgroups of odd index in finite groups with simple classical socle.
Introduction
The subgroup of a finite group G generated by the set of all its minimal non-trivial normal subgroups is called the socle of G and is denoted by Soc(G). A finite group is almost simple if its socle is a nonabelian simple group. It is well known that a finite group G is almost simple if and only if there exists a nonabelian finite simple group L such that L ≃ Inn(L) ⊴ G ≤ Aut(L). In this case Inn(L) = Soc(G). One of the greatest results in the theory of finite permutation groups was obtained by Liebeck and Saxl [7] and independently by Kantor [3]. They gave the classification of finite primitive permutation groups of odd degree. In particular, for each finite group G whose socle is a simple classical group they specified types of subgroups which can be maximal subgroups of odd index in G. However, not every subgroup of these types is a maximal subgroup of odd index in G. Thus, the classification of maximal subgroups of odd index in finite groups with a simple classical socle is not complete. In this paper, we discuss the completion of the classification of maximal subgroups of odd index in finite groups with simple classical socle.
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.