Maximal subgroups of small index of finite almost simple groups

A Classification of the Maximal Subgroups of the Finite Alternating ...

subgroups of the almost simple groups-that is, of groups X such that. X0 u X< Aut X, for some finite non-abelian simple group X0. The problem has been solved ...

Probabilistic and asymptotic aspects of finite simple groups

Despite being “known”, the non-almost simple maximal subgroups can have ... number of maximal subgroups of index n in the finite group G. Define. µ(G) ...

The symmetric group, 11 | Peter Cameron's Blog - WordPress.com

... maximal subgroups of small index will need more care than those of large index. ... almost simple groups, and especially to simple groups.

Computing subgroups of bounded index in a finite group - CiteSeerX

In either case, we make use of databases containing information about the subgroups of almost simple groups of small order. If G/L has simple composition ...

FINITE GROUPS

... finite groups: maximal subgroups and ordinary characters for simple groups. ... For the smaller families, this has had the effect that the last group ...

maximal subgroups of finite groups - UFDC Image Array 2

maximal subgroups of small finite simple groups are listed in the Atlas of Finite Groups ... (6) An almost simple group acting on the cosets of a maximal subgroup ...

from simple groups to maximal subgroups - SEIS

There is an absolute constant c such that any maximal subgroup of a finite almost simple group has at most nc maximal subgroups of index n. This yields a ...

Book:Robert A. Wilson/The Finite Simple Groups - ProofWiki

1 The alternating groups: 2.2. · 2 Transitivity: 2.2. · 3 Primitivity: 2.2. · 4 Group actions: 2.2. · 5 Maximal subgroups: 2.2. · 6 Wreath products.

ALMOST SIMPLE GROUPS

Properties of Finite Groups Of Lie Type Maximal Subgroups of the Classical Groups Maximal Subgroups of the Exceptional Groups Sylow ...

Applying the Classification of Finite Simple Groups

... almost-simple group Sn, we are in effect “reducing” in (6) to determining maximal subgroups such as Hα for all almost-simple groups. Exercise 6.1.2. Which ...

A classification of the maximal subgroups of the finite alternating and ...

We determine upper bounds for the maximum order of an element of a finite almost simple group with socle T in terms of the minimum index m(T) of a maximal ...

MAXIMAL SUBGROUPS OF FINITE CLASSICAL GROUPS AND ...

However, their analysis relies heavily upon the classification of finite simple groups. Various authors, too many to be quoted here, have used Aschbacher's.

List of finite simple groups - Wikipedia

In mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of ...

On Groups with Countably Many Maximal Subgroups.

The next result is almost the only property shared by all CG- groups. Lemma 2. If G is a CG-group, every maximal subgroup of G has countable index. Proof. Let M ...

THE SIMPLE REE GROUPS 2F4(q2) ARE DETERMINED BY ... - Kent

(b) If K is a maximal subgroup of Sz(q2) whose index divides some nontrivial character degree of Sz(q2) or (q2 −1)2, then K is a Frobenius group of index q4 +1.

MAXIMAL SUBGROUPS OF THE SPORADIC ALMOST-SIMPLE ...

Then H is the normalizer in G of a direct product of isomorphic simple groups. We will need a lemma: Lemma 1.7 Let K be a finite group with no characteristic ...

Finite Groups with Exactly Two Maximal Subgroups are Cyclic

Answering a viewer question, we prove that every finite group with exactly two maximal subgroups is cyclic. Along the way, we define maximal ...

The Maximal Subgroups of the Low-Dimensional Finite Classical ...

... maximal subgroups of the almost simple finite exceptional groups that have faithful representations of degree at most 12. A group G is simple ...

Maximal Subgroups of a Finite Group - PNAS

numbers which divide the order of G and the k maximal subgroups of G correspond to thesubgroups of prime index in this quotient group. When k = 1 and the order ...

Finite Groups and Almost Free Actions - jstor

In the case p < f one obtains an abelian normal subgroup of f-bounded index ... maximal subgroups of finite simple groups. The groups in case 1 are of ...