相关论文: Extension of a residually finite group by a residu…

We give a structural theorem for pseudofinite groups of finite centraliser dimension. As a corollary, we observe that there is no finitely generated pseudofinite group of finite centraliser dimension.

We introduce a generalization of the product expansion of a finite semigroup. As an application, we provide an alternative proof of the decidability of pointlike sets for pseudovarieties consisting of semigroups whose subgroups all belong…

In this work, we prove that every SFT, sofic shift, and strongly irreducible shift on locally finite groups has strong dynamical properties. These properties include that every sofic shift is an SFT, every SFT is strongly irreducible, every…

In this article we study a class of central extensions of $\mathbb{Z}\wr\mathbb{Z}$, as first described by Hall. On the one hand, we consider groups of this type with cyclic centre, our construction yields a rich class of groups. In…

We prove that if the group of fixed points of a generic automorphism of a simple group of finite Morley rank is pseudofinite, then this group is an extension of a (twisted) Chevalley group over a pseudofinite field. On the way to obtain…

We prove that a hyperbolic group admits a strongly aperiodic subshift of finite type if and only if it has at most one end.

A classical result of Halmos asserts that among measure preserving transformations the weak mixing property is generic. We extend Halmos' result to the collection of ergodic extensions of a fixed, but arbitrary, ergodic transformation…

We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable relatively hyperbolic group is residually finite. As a direct consequence, we obtain that the outer automorphism group of a limit…

We prove that finite partial orders with a linear extension form a Ramsey class. Our proof is based on the fact that class of acyclic graphs has the Ramsey property and uses the partite construction.

In this note, we verify that several fundamental results from the theory of representations of reductive $p$-adic groups, extend to finite central extensions of these groups.

We prove that the weak order on an infinite Coxeter group contains infinite antichains if and only if the group is not affine.

We provide an example of a non-finitely generated group which admits a nonempty strongly aperiodic SFT. Furthermore, we completely characterize the groups with this property in terms of their finitely generated subgroups and the roots of…

We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…

We define sofic, weakly sofic, linear sofic and hyperlinear metric groups and discuss some issues involving axiomatizability of these classes in continuous logic.

We prove that any finitely generated one ended group has linear end depth. Moreover, we give alternative proofs to theorems relating the growth of a finitely generated group to the number of its ends.

A weakly U abundant is a class of semigroups characterized using some generalized Green' relations. In this paper we discuss the variants of weakly U - abundant semigroups and it is shown that the idempotent variants of these semigroups are…

In this paper, a group is called weakly amenable if its left regular representation is not uniformly isolated from the trivial representation. First examples of finitely generated non-amenable weakly amenable groups are constructed.

Every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) is finitely presented and residually finite.

We prove that representations of the braid groups coming from weakly group-theoretical braided fusion categories have finite images.

In this article we introduce the notion of weak identities in a group and study their properties. We show that weak identities have some similar properties to ordinary ones. We use this notion to prove that any finitely generated solvable…