Related papers: Normal subgroups generated by a single polynomial …

Given two convex polytopes, the join, the cartesian product and the direct sum of them are well understood. In this paper we extend these three kinds of products to abstract polytopes and introduce a new product, called the topological…

There has been considerable interest in recent decades in questions of random generation of finite and profinite groups, and finite simple groups in particular. In this paper we study similar notions for finite and profinite associative…

Let $G$ be a finite group and $N$ a normal subgroup of $G$. We determine the structure of $N$ when the diameter of the graph associated to the $G$-conjugacy classes contained in $N$ is as large as possible, that is, is equal to three.

A generalized quadrangle is a point-line incidence geometry such that any two points lie on at most one line and, given a line $\ell$ and a point $P$ not incident with $\ell$, there is a unique point of $\ell$ collinear with $P$. We study…

Trinomial hypersurfaces form a natural class of affine algebraic varieties closely connected with varieties admitting a torus action of complexity one. We investigate orbits of the automorphism group on these hypersurfaces. We prove that…

Given a polynomial endomorphism F of the n-dimensional affine space over a field K, we define a sequence of polynomial endomorphisms of the affine space associated to F. We call F nice if there exists an integer m such that the m-th term of…

The principal filtration of the infinite-dimensional odd Contact Lie superalgebra over a field of characteristic $p>2$ is proved to be invariant under the automorphism group by investigating ad-nilpotent elements and determining certain…

A group is boundedly simple if, for some constant N, every nontrivial conjugacy class generates the whole group in N steps. For a large class of trees, Tits proved simplicity of a canonical subgroup of the automorphism group, which is…

Let $\phi \in \mbox{Out}(F_n)$ be a free group outer automorphism that can be represented by an expanding, irreducible train-track map. The automorphism $\phi$ determines a free-by-cyclic group $\Gamma=F_n \rtimes_\phi \mathbb Z,$ and a…

Any simple pseudofinite group G is known to be isomorphic to a (twisted) Chevalley group over a pseudofinite field. This celebrated result mostly follows from the work of Wilson in 1995 and heavily relies on the classification of finite…

Given a von Neumann algebra $M$ we consider the central extension $E(M)$ of $M.$ For type I von Neumann algebras $E(M)$ coincides with the algebra $LS(M)$ of all locally measurable operators affiliated with $M.$ In this case we show that an…

We construct free abelian subgroups of the group $U(A_\Gamma)$ of untwisted outer automorphisms of a right-angled Artin group, thus giving lower bounds on the virtual cohomological dimension. The group $U(A_\Gamma)$ was previously studied…

Let $Aut_{alg}(X)$ be the subgroup of the group of regular automorphisms $Aut(X)$ of an affine algebraic variety $X$ generated by all connected algebraic subgroups. We prove that if $dim X \ge 2$ and if $Aut_{alg}(X)$ is rich enough,…

Sturmfels-Sullivant conjectured that the cut polytope of a graph is normal if and only if the graph has no K_5 minor. In the present paper, it is proved that the normality of cut polytopes of graphs is a minor closed property. By using this…

We compute explicitly the automorphism and outer automorphism group of all large-type free-of-infinity Artin groups. Our strategy involves reconstructing the associated Deligne complexes in a purely algebraic manner, i.e. in a way that is…

We construct four infinite families of chiral $3$-polytopes of type $\{4, 8\}$, with $1024m^4$, $2048m^4$, $4096m^4$ and $8192m^4$ automorphisms for every positive integer $m$, respectively. The automorphism groups of these polytopes are…

Let K be an algebraically closed field of characteristic zero. We say that a polynomial automorphism f : K^n -> K^n is special if the Jacobian of f is equal to 1. We show that every (n - 1)-dimensional component H of the set Fix(f) of fixed…

For a subshift over a finite alphabet, a measure of the complexity of the system is obtained by counting the number of nonempty cylinder sets of length $n$. When this complexity grows exponentially, the automorphism group has been shown to…

We construct four-dimensional gravity theories that resolve the Schwarzschild singularity and enable dynamical studies of nonsingular gravitational collapse. The construction employs a class of nonpolynomial curvature invariants that…

For a finite alphabet $\mathcal{A}$ and shift $X\subseteq\mathcal{A}^{\mathbb{Z}}$ whose factor complexity function grows at most linearly, we study the algebraic properties of the automorphism group ${\rm Aut}(X)$. For such systems, we…