Second maximal subgroups of the finite alternating and symmetric groups

Details Second maximal subgroups of the finite alternating and symmetric groups Second maximal subgroups of the finite alternating and symmetric groups

2008-10-21

arxiv.org/abs/0810.3721v1

Mathematics

Group Theory

The PhD thesis of the author (The Australian National University, Canberra)

Scientific paper

A subgroup of a finite group G is said to be second maximal if it is maximal in every maximal subgroup of G that contains it. A question which has received considerable attention asks: can every positive integer occur as the number of the maximal subgroups that contain a given second maximal subgroup in some finite group G? Various reduction arguments are available except when G is almost simple. Following the classification of the finite simple groups, finite almost simple groups fall into three categories: alternating and symmetric groups, almost simple groups of Lie type, sporadic groups and automorphism groups of sporadic groups. This thesis investigates the finite alternating and symmetric groups, and finds that in such groups, except three well known examples, no second maximal subgroup can be contained in more than 3 maximal subgroups.

Affiliated with

Also associated with

No associations

Rating

Second maximal subgroups of the finite alternating and symmetric groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Second maximal subgroups of the finite alternating and symmetric groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Second maximal subgroups of the finite alternating and symmetric groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-572430