Related papers: Introduction to Sporadic Groups

We introduce a linearly ordered lattice $\mu(Grp)$ of torsion theories in simplicial groups. The torsion theories are defined where the torsion/torsion-free subcategories are given by the simplicial groups with bounded above/below Moore…

We find the nonabelian finite simple groups with order prime divisors not exceeding 1000. More generally, we determine the sets of nonabelian finite simple groups whose maximal order prime divisor is a fixed prime less than 1000. Our…

We present explicit upper bounds for the number and size of conjugacy classes in finite Chevalley groups and their variations. These results have been used by many authors to study zeta functions associated to representations of finite…

In this paper we introduce and study the lattice of normal subgroups of a group $G$ that determine solitary quotients. It is closely connected to the well-known lattice of solitary subgroups of $G$ (see \cite{5}). A precise description of…

The goal of this paper is to describe a theoretical construction of an infinite collection of non-classical Schottky groups. We first show that there are infinitely many non-classical noded Schottky groups on the boundary of Schottky space,…

This paper is concerned with random walks on a family of dyadic-valued solvable matrix groups. A description of the Poisson boundary of these groups for probability measures of finite first moment and non-zero displacements (or drifts) is…

In this short note we introduce a new metric on certain finite groups. It leads to a class of groups for which the element orders satisfy an interesting inequality. This extends the class CP_2 studied in our previous paper [16].

We introduce and study the class of spherically ordered groups. The notions of spherically ordered groups and their spectra of spherical orderability are introduced. Values of these spectra are found for a series of natural groups.

Among the infinite classes of finite simple groups, the most exotic classes are probably the Suzuki groups and the Ree groups. They are "twisted versions" of groups of Lie type, but they cannot be directly obtained as groups of rational…

In 1934, Garrett Birkhoff has shown that the number of isomorphism classes of finite metabelian groups of order $p^{22}$ tends to infinity with $p$. More precisely, for each prime number $p$ there is a family…

Many groups possess highly symmetric generating sets that are naturally endowed with an underlying combinatorial structure. Such generating sets can prove to be extremely useful both theoretically in providing new existence proofs for…

We construct a family of infinite simple groups that we call \emph{twisted Brin-Thompson groups}, generalizing Brin's higher-dimensional Thompson groups $sV$ ($s\in\mathbb{N}$). We use twisted Brin-Thompson groups to prove a variety of…

We exhibit a new presentation of the (equilateral) Von Dyck groups $D(2,3,n), \ n\ge 3$, in terms of two generators of order $n$ satisfying three relations, one of which is Artin's braid relation. By dropping the relation which fixes the…

As a consequence of the classification of finite simple groups, the classification of permutation groups of prime degree is complete, apart from the question of when the natural degree $(q^n-1)/(q-1)$ of ${\rm L}_n(q)$ is prime. We present…

The notion of simple compact quantum group is introduced. As non-trivial (noncommutative and noncocommutative) examples, the following families of compact quantum groups are shown to be simple: (a) The universal quantum groups $B_u(Q)$ for…

A finite transitive permutation group is said to be 3/2-transitive if all the nontrivial orbits of a point stabilizer have the same size greater than 1. Examples include the 2-transitive groups, Frobenius groups and several other less…

Let $\mathbb{M}$ be the monster group which is the largest sporadic finite simple group, and has first been constructed in 1982 by Griess. In 1985, Conway has constructed a 196884-dimensional representation $\rho$ of $\mathbb{M}$ with…

This document gives a list of finite semigroups that are interesting from the point of view of Krohn-Rhodes complexity theory. The list will be expanded and updates as "time goes by".

We refer to the set of the orders of elements of a finite group as its spectrum and say that finite groups are isospectral if their spectra coincide. In the paper we determine all finite groups isospectral to the simple groups $S_6(q)$,…

The set of prime numbers $p$ such that the supersingular $j$-invariants in characteristic $p$ are all contained in the prime field is finite. And it is well known that this set of primes coincides with the set of prime divisors of the order…