Related papers: Maximal subgroups of sporadic groups

Automorphism groups of $2$-groups of coclass at most $3$ are investigated.

Let G be a group. We say that G has spread r if for any set of distinct elements {x1,..., xr}\subset G there exists an element y\in G with the property that <xi, y>=G for every 0<i<r+1. Few bounds on the spread of finite simple groups are…

We study finite groups which possess a strongly p-embedded subgroup for some odd prime p. The main results of the paper will be applied in the ongoing project to classify the simple groups of local characteristic p.

Together with their 1988 construction of the monster vertex algebra $V^\natural$, Frenkel, Lepowsky, and Meurman showed that the largest sporadic simple group, known as the Fischer-Griess monster, forms the symmetry group of an infinite…

Finite groups with given systems of permuteral and strongly permuteral subgroups are studied. New characterizations of w-supersoluble and supersoluble groups are received.

We revisit the known problem whether each compact topology is contained in a maximal compact topology and collect some partial answers to this question. For instance we show that each compact topology is contained in a compact topology in…

We prove that every countable subgroup of a compact metrizable abelian group has a characterizing set. As an application, we answer several questions on maximally almost periodic (MAP) groups and give a characterization of the class of…

The groups of order 64p without a normal sylow p-subgroup are listed, and their automorphism groups are also determined. As a by-product of our original effort to get these groups, we needed to determine the automorphism groups of those…

In 1962, V.A. Belonogov proved that if a finite group $G$ contains two maximal subgroups of coprime orders, then either $G$ is one of known solvable groups or $G$ is simple. In this short note based on results by M. Liebeck and J. Saxl on…

In this article, we study symmetric designs admitting flag-transitive, point-imprimitive almost simple automorphism groups with socle sporadic simple groups. As a corollary, we present a classification of symmetric designs admitting…

We study adequate subgroups of $GL_n$ over a finite field. This notion is useful in the study of automorphy lifting theorems. In particular, we give a sufficient condition for a subgroup to be adequate.

This is the written version of the Bourbaki seminar given in January 2013 and published in 2014 (modulo an additional early reference added subsequently). It describes the first construction of infinite, finitely generated amenable simple…

The author determines the structure of automorphism groups of smooth plane curves of degree at least four. Furthermore, he gives some upper bounds for the order of automorphism groups of smooth plane curves and classifies the cases with…

We exhibit examples of groups of intermediate growth with $2^{\aleph_0}$ ergodic, continuous, invariant random subgroups. The examples are the universal groups associated with a family of groups of intermediate growth.

We use topological methods to study the maximal subgroups of the free idempotent generated semigroup on a biordered set. We use these to give an example of a free idempotent generated semigroup with maximal subgroup isomorphic to the free…

We give a classification of maximal elements of the set of finite groups that can be realized as the full automorphism groups of simple polarized abelian fourfolds over finite fields. As an application, we compute the Jordan constants of…

This paper investigates the finite generation of cluster automorphism groups. By applying the pseudo $\mathbb{N}$-grading introduced in our previous work, we establish a sufficient condition for a cluster automorphism group to be finitely…

We study finite p-groups G of coclass upto 4 for which the group Aut_z(G) of all central automorphisms of G is of minimal possible order. As a consequence, we obtain very short and elementary proofs of main results of Sharma and Gumber [7].

We study automorphism groups of smooth quintic threefolds. Especially, we describe all the maximal ones with explicit examples of target quintic threefolds. There are exactly $22$ such groups.

We obtain necessary and sufficient conditions when a pseudocompact paratopological group is topological. (2-)pseudocompact and countably compact paratopological groups that are not topological are constructed. It is proved that each…