✦ LIBER ✦

Maximal Subgroups of Symmetric Groups

✍ Scribed by Martin W. Liebeck; Aner Shalev

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 348 KB
Volume: 75
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1996.0082

No coin nor oath required. For personal study only.

✦ Synopsis

We show that S n has at most n 6Â11+o(1) conjugacy classes of primitive maximal subgroups. This improves an n c log 3 n bound given by Babai. We conclude that the number of conjugacy classes of maximal subgroups of S n is of the form ( 12 +o(1))n. It also follows that, for large n, S n has less than n ! maximal subgroups. This confirms a special case of a conjecture of Wall. Improving a recent result from [MSh], we also show that any finite almost simple group has at most n 17Â11+o(1) maximal subgroups of index n.

📜 SIMILAR VOLUMES

Generating Finite Groups with Maximal Su

Generating Finite Groups with Maximal Subgroups of Maximal Subgroups

✍ P. Flavell 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 475 KB

Characters of Maximal Subgroups ofM-Grou

Characters of Maximal Subgroups ofM-Groups

✍ Mark L. Lewis 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 348 KB

Maximal Unipotent Subgroups of Finitary

Maximal Unipotent Subgroups of Finitary Linear Groups

✍ Orazio Puglisi 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 326 KB

Symmetrical Subgroups of Artin Groups

✍ John Crisp 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 208 KB

We show that the subgroup fixed by a group of symmetries of an Artin system (A, S) is itself an Artin group under the hypothesis that the Deligne complex associated to A admits a suitable CAT(0) metric. Such a metric is known to exist for all Artin groups of type FC, which include all the finite typ

c-Sections of Maximal Subgroups of Finit

c-Sections of Maximal Subgroups of Finite Groups

✍ Yanming Wang; Li Shirong 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 88 KB

Let G be a finite group and let M be a maximal subgroup of G. Let K/L be a chief factor of G such that L ≤ M and G = MK. We call the group M ∩ K/L a c-section of M in G. All c-sections of M are isomorphic. Using the concept of c-sections, we obtain some new characterizations of solvable and π-solvab

Conjugacy Classes in Maximal Parabolic S

Conjugacy Classes in Maximal Parabolic Subgroups of General Linear Groups

✍ Scott H. Murray 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 184 KB

We compute conjugacy classes in maximal parabolic subgroups of the general linear group. This computation proceeds by reducing to a "matrix problem." Such problems involve finding normal forms for matrices under a specified set of row and column operations. We solve the relevant matrix problem in sm