Related papers: Finite simple groups of Lie type as expanders

We construct words with small image in a given finite alternating or unimodular group. This shows that word width in these groups is unbounded in general.

These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.

We prove that the length of the shortest identity in a finite simple group of Lie type of rank $r$ defined over $\mathbb{F}_q$, is bounded (from above and below) by explicit polynomials in $q$ and $r$.

Following Sullivan's spacial realization of a differential algebra, we construct a universal integrating Lie 2-groupoid for every Lie algebroid. Then We show that unlike Lie algebras which one-to-one correspond to simply connected Lie…

Methods from additive number theory are applied to construct families of finitely generated linear semigroups with intermediate growth.

We compute the number of orbit types for simply connected simple algebraic groups over algebraically closed fields as well as for compact simply connected simple Lie groups. We also compute the number of orbit types for the adjoint action…

We classify, up to conjugacy, the finite (constant) subgroups G of adjoint absolutely simple algebraic groups of type $A_1$ over an arbitrary field $k$ of characteristic not 2.

We present a characterization of finite permutation groups which contain a transitive dihedral subgroup.

We provide the first example of a finitely presented, and the first example of a simple, group of non-uniform exponential growth. The example is given by Thompson's group V.

We study actions of linear algebraic groups on finite-dimensional central simple algebras. We describe the fixed algebra for a broad class of such actions.

For every finite abelian group $G$, there are positive integers $n$ and $d$ such that $G$ is isomorphic to the multiplicative group of $d$-th powers of reduced residues modulo $n$.

We classify abelian subgroups of the automorphism group of any compact simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup. This leads to a classification of the maximal abelian subgroups of compact…

All simple weight modules with finite dimensional weight spaces over affine Lie algebras are classified.

In this note we study the finite groups whose subgroup lattices are dismantlable.

This is the fourth one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with orthogonal groups of minus type.

A version of Paley-Wiener like theorem for connected, simply connected nilpotent Lie groups is proven.

We show that countable direct limits of finite-dimensional Lie groups do not have small subgroups. The same conclusion is obtained for suitable direct limits of infinite-dimensional Lie groups.

We introduce anyonic Lie algebras in terms of structure constants. We provide the simplest examples and formulate some open problems.

In this paper we present new examples of simple $p$-local compact groups for all odd primes. We also develop the necessary tools to show saturation, simpleness and the non-realizability as $p$-compact groups or compact Lie groups, which can…

We give a description of non-growing subsets in linear groups, which extends the Product theorem for simple groups of Lie type. We also give an account of various related aspects of growth in linear groups.