相关论文: Shadowing for families of endomorphisms of general…

Given a finite connected simple graph $\Gamma$, and a subgroup $G$ of its automorphism group, a general method for finding all finite abelian regular coverings of $\Gamma$ that admit a lift of each element of $G$ is developed. As an…

We classify all the $2$-arc-transitive strongly regular graphs, and use this classification to study the family of finite $(G,3)$-geodesic-transitive graphs of girth $4$ or $5$ for some group $G$ of automorphisms. For this application we…

The article $-$ part of a larger thesis which aims to give a detailed description of the generalisation to the category of groups with operators of the classical theory of semisimplicity for modules $-$ presents a straightforward…

We prove two conjectures on the automorphism group of a one-dimensional formal group law defined over a field of positive characteristic. The first is that if a series commutes with a nontorsion automorphism of the formal group law, then…

The inner automorphisms of a group G can be characterized within the category of groups without reference to group elements: they are precisely those automorphisms of G that can be extended, in a functorial manner, to all groups H given…

We show that every algebraic group scheme over a field with at least 8 elements can be realized as the group of automorphisms of a nonassociative algebra. This is only a modest improvement of the theorem of Gordeev and Popov (2003), but it…

A generalized numerical semigroup is a submonoid $S$ of $\mathbb{N}^d$ with finite complement in it. We characterize isomorphisms between these monoids in terms of permutation of coordinates. Considering the equivalence relation that…

Suppose $(X,\sigma)$ is a subshift, $P_X(n)$ is the word complexity function of $X$, and ${\rm Aut}(X)$ is the group of automorphisms of $X$. We show that if $P_X(n)=o(n^2/\log^2 n)$, then ${\rm Aut}(X)$ is amenable (as a countable,…

Let $(X_A,\sigma_A)$ be the right one-sided topological Markov shift for an irreducible matrix with entries in $\{0,1\}$, and $\Gamma_A$ the continuous full group of $(X_A,\sigma_A)$. For two irreducible matrices $A$ and $B$ with entries in…

In the following text for arbitrary $X$ with at least two elements, nonempty set $\Gamma$ and self-map $\varphi:\Gamma\to\Gamma$ we prove the set-theoretical entropy of generalized shift $\sigma_\varphi:X^\Gamma\to X^\Gamma$…

Let $\Gamma$ be a group of type rotating automorphisms of a building $\cB$ of type $\widetilde A_2$, and suppose that $\Gamma$ acts freely and transitively on the vertex set of $\cB$. The apartments of $\cB$ are tiled by triangles, labelled…

Cluster automorphisms have been shown to have links to the mapping class groups of surfaces, maximal green sequences and to exchange graph automorphisms for skew-symmetric cluster algebras. In this paper we aim to generalise these results…

We develop an explicit covering theory for complexes of groups, parallel to that developed for graphs of groups by Bass. Given a covering of developable complexes of groups, we construct the induced monomorphism of fundamental groups and…

Let G be a finite group scheme over an algebraically closed field of positive characteristic. Assume further that the connected component of G is unipotent. It is shown that the projectivity of a rational G-module can be detected on a…

If $\Gamma $ is a group, then braided $\Gamma $-crossed modules are classified by braided strict $\Gamma $-graded categorial groups. The Schreier theory obtained for $\Gamma $-module extensions of the type of an abelian $\Gamma $-crossed…

Let \alpha be an automorphism of the totally disconnected group G. The compact open subgroup, V, if G is tidy for \alpha if [\alpha(V') : \alpha(V')\cap V'] is minimised at V, where V' ranges over all compact open subgroups of G.…

The regular objects in various categories, such as maps, hypermaps or covering spaces, can be identified with the normal subgroups N of a given group \Gamma, with quotient group isomorphic to \Gamma/N. It is shown how to enumerate such…

We consider integrability properties of the superstring on $AdS_{5}\times S^{5}$ background and construct a new one parameter family of currents which satisfies the vanishing curvature condition. We present the Hamiltonian analysis for the…

The concept of modulation is generalized to pseudo-modulation and its subclasses including pre-modulation, generalized modulation and regular modulation. The motivation is to define the valued analogue of natural quiver, called {\em natural…

Let T be a k-regular tree (k>2) and A its automorphism group. We analyze a generic finitely generated subgroup Gamma of A. We show that Gamma is free and establish a trichotomy on the closure of Gamma: it is either discrete, compact or has…