Related papers: Cherlin's conjecture for sporadic simple groups

We classify all infinite primitive permutation groups possessing a finite point stabilizer, thus extending the seminal Aschbacher-O'Nan-Scott Theorem to all primitive permutation groups with finite point stabilizers.

A transitive permutation group of prime degree is doubly transitive or solvable. We give a direct proof of this theorem by Burnside which uses neither S-ring type arguments, nor representation theory.

We prove a natural generalization of Szep's conjecture. Given an almost simple group $G$ with socle not isomorphic to an orthogonal group having Witt defect zero, we classify all possible group elements $x,y\in G\setminus\{1\}$ with $G={\bf…

We give a simple proof of the Lalonde-McDuff conjecture for aspherical manifolds.

We prove the Morrison--Kawamata cone conjecture for projective primitive symplectic varieties with $\Q$-factorial and terminal singularities with $b_2\geq 5$, from which we derive for instance the finiteness of minimal models of such…

The Herzog-Sch\"onheim conjecture states that if $H_1, \ldots, H_k$ are subgroups of a group $G$ and $x_1, \ldots, x_k$ are elements of $G$ such that $H_1x_1, \ldots, H_kx_k$ is a partition of $G$ into cosets, then two of these subgroups…

Motivated in part by representation theoretic questions, we prove that if G is a finite quasi-simple group, then there exists an elementary abelian subgroup of G that intersects every conjugacy class of involutions of G.

We investigate the proportion of fixed point free permutations (derangements) in finite transitive permutation groups. This article is the first in a series where we prove a conjecture of Shalev that the proportion of such elements is…

We extend a conjecture of Kimberley-Robertson on the abelianizations of certain square complex groups.

Using the classification of finite simple groups we prove Alperin's weight conjecture and the character theoretic version of Broue's abelian defect group conjecture for 2-blocks of finite groups with an elementary abelian defect group of…

Let $G$ be a primitive permutation group of degree $n$ with nonabelian socle, and let $k(G)$ be the number of conjugacy classes of $G$. We prove that either $k(G)<n/2$ and $k(G)=o(n)$ as $n\rightarrow \infty$, or $G$ belongs to explicit…

Let $G$ be a finite permutation group on $\Omega$. An ordered sequence $(\omega_1,\ldots,\omega_\ell)$ of elements of $\Omega$ is an irredundant base for $G$ if the pointwise stabilizer is trivial and no point is fixed by the stabilizer of…

We prove a conjecture of R. Schwartz about the type of some complex hyperbolic triangle groups.

The primitive finite permutation groups containing a cycle are classified. Of these, only the alternating and symmetric groups contain a cycle fixing at least three points. The contributions of Jordan and Marggraff to this topic are briefly…

In this paper, we prove the K- and L-theoretical Isomorphism Conjecture for Baumslag-Solitar groups with coefficients in an additive category.

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 ${\rm PSL}_n(q)$ is prime. We…

We prove the Farrell-Jones conjecture for free-by-cyclic groups. The proof uses recently developed geometric methods for establishing the Farrell-Jones Conjecture.

This is the first of three articles on the Fibered Isomorphism Conjecture of Farrell and Jones for L-theory. We apply the general techniques developed in [15] and [16] to the L-theory case of the conjecture and prove several results. Here…

Let $G$ be a transitive permutation group on a set $\Omega$, and suppose $G_{\alpha}\cap G_{\beta}=1$ for some distinct $\alpha, \beta\in\Omega$. The Saxl graph $\Sigma(G)$ of $(G, \Omega)$ is defined as the graph with vertex set $\Omega$,…

We define a translation based cipher over an arbitrary finite field, and study the permutation group generated by the round functions of such a cipher. We show that under certain cryptographic assumptions this group is primitive. Moreover,…