相关论文: An automorphism group of an omega-stable structure…

We consider automorphism groups of some countably categorical structures and their precompact expansions. We prove that automorphism groups of omega-stable omega-categorical structures have metrizable universal minimal flows. We also study…

We analyse omega-categorical precompact expansions of particular omega-categorical structures from the viewpoint of amenability of their automorphism groups. The main result of the paper corrects and simplifies Section 3.2 of the first…

The first-order theory of the automorphism group of an infinite resplendent model in a finite language is undecidable.

A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of maps, hypermaps, dessins, polytopes and covering spaces, where…

We show that the group of type-preserving automorphisms of any irreducible semi-regular thick right-angled building is abstractly simple. When the building is locally finite, this gives a large family of compactly generated (abstractly)…

In this paper we study the existence of at least one non-inner automorphism of order p in a finite normally constrained p-group when p is an odd prime.

We introduce a strategy to study irreducible representations of automorphism groups of finite modules over local rings. We prove that these automorphism groups fit in a hierarchy that facilitates a stratification of their irreducible…

We investigate some situation in which automorphisms of a group G are uniquely determined by their restrictions to a proper subgroup H. Much of the paper is devoted to studying under which additional hypotheses this property forces G to be…

A topological group $G$ is said to have a local $\omega^\omega$-base if the neighbourhood system at identity admits a monotone cofinal map from the directed set $\omega^\omega$. In particular, every metrizable group is such, but the class…

In this paper we study families of representations of the outer automorphism groups indexed on a collection of finite groups $\mathcal{U}$. We encode this large amount of data into a convenient abelian category $\mathcal{A}\mathcal{U}$…

We investigate the structure of the monoid of endomorphisms of the ordered set $(\mathbb{Q},{\leq})$ of rational numbers. We show that for any countable linearly ordered set $\Omega$, there are uncountably many maximal subgroups of…

In this work the problem about an existence of non-measurable automorphisms of Lie groups finite and as well infinite dimensional over the field of real numbers and also over the non-archimedean local fields is investigated.…

Solecki proved that the group of automorphisms of a countable structure cannot be an uncountable free abelian group. See more in Just, Shelah and Thomas math.LO/0003120 where as a by product we can say something on on uncountable…

We study upper bounds on the order of automorphisms of non-singular curves $X$ satisfying at least one of the following hypothesis: 1) $X$ is an $m$-sheeted covering of exactly one non-singular curve of genus $\gamma$, where $m$ is prime;…

Answering a question of Junker and Ziegler, we construct a countable first order structure which is not omega-categorical, but does not have any proper non-trivial reducts, in either of two senses (model-theoretic, and group-theoretic). We…

We show that the automorphism groups of countably categorical linear orders are extremely amenable. Using methods of Kechris, Pestov, and Todorcevic, we use this fact to derive a structural Ramsey theorem for certain families of finite…

We are concerned with orderable groups and particularly those with orderings invariant not only under multiplication, but also under a given automorphism or family of automorphisms. Several applications to topology are given: we prove that…

We study automorphism groups of randomizations of separable structures, with focus on the $\aleph_0$-categorical case. We give a description of the automorphism group of the Borel randomization in terms of the group of the original…

We show that if a nontrivial group admits a locally invariant ordering, then it admits uncountably many locally invariant orderings. For the case of a left-orderable group, we provide an explicit construction of uncountable families of…

In this paper we study the existence of at least one non-inner automorphism of order p of a finite thin p-group, for any prime p.