Related papers: On the first-order genus of wreath products and th…

We suggest a criterion under which for a nilpotent group of finite exponent $A$ and for an abelian group $B$ the variety $var(A \,Wr\, B)$ generated by their wreath product $A \,Wr\, B$ is equal to the product of varieties $var(A)$ and…

A finitely generated group is said to be an automata group if it admits a faithful self-similar finite-state representation on some regular $m$-tree. We prove that if $G$ is a subgroup of an automata group, then for each finitely generated…

We prove that if a subgroup $H$ of the automorphism group $\mathrm{Aut}(\Sigma^{\mathbb{Z}})$ of a non-trivial full shift acts on points of finite support with a free orbit, then for every finitely-generated abelian group $A$, the abstract…

We prove that the category of $\mathbb{Z}_2 ^n$-manifolds has all finite products. Further, we show that a $\mathbb{Z}_2 ^n$-manifold (resp., a $\mathbb{Z}_2 ^n$-morphism) can be reconstructed from its algebra of global $\mathbb{Z}_2…

In this paper we consider Chevalley groups over commutative rings with~$1$, constructed by irreducible root systems of rank $>1$. We always suppose that for the systems $A_2, B_\ell, C_\ell, F_4, G_2$ our rings contain $1/2$ and for the…

Let $V$ be a quasi-conformal grading-restricted vertex algebra, $W$ be its module, and $\W_{z_1, \ldots, z_n}$ be the space of rational differential forms with complex parameters $(z_1, \ldots, z_n)$ for $n \ge 0$. Using geometric…

We show that the wreath product $G \wr \mathbb{Z}^n$ of any finitely generated group $G$ with $\mathbb{Z}^n$ has finite palindromic width. We also show that $C \wr A$ has finite palindromic width if $C$ has finite commutator width and $A$…

Let $G$ be an abelian group of order $n$ and let $R$ be a commutative ring which admits a homomorphism ${\Bbb Z}[\zeta_{n}]\ra R$, where $\zeta_{n}$ is a (complex) primitive $n$-th root of unity. Given a finite $R[G\e]$-module $M$, we…

We prove that for many nonamenable groups \Gamma, including all hyperbolic groups and all nontrivial free products, the left-right wreath product group G := (Z/2Z)^(\Gamma) \rtimes (\Gamma \times \Gamma) is W*-superrigid. This means that…

An example of an extension of a completely simple semigroup U by a group H is given which cannot be embedded into the wreath product of U by H. On the other hand, every central extension of U by H is shown to be embeddable in the wreath…

Let $R$ be a semilocal principal ideal domain. Two algebraic objects over $R$ in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all…

In this paper, we show that wreath products of groups have linear divergence, and we generalise the argument to permutational wreath products. We also prove that Houghton groups $\mathcal{H}_m$ with $m\geq 2$ and Baumslag-Solitar groups…

If $\Gamma$ is an irreducible non-uniform higher-rank characteristic zero arithmetic lattice (for example, $SL_n(\mathbb{Z})$, $n \geq 3$) and $\Lambda$ is a finitely generated group that is elementarily equivalent to $\Gamma$, then…

From any two median spaces $X,Y$, we construct a new median space $X \circledast Y$, referred to as the diadem product of $X$ and $Y$, and we show that this construction is compatible with wreath products in the following sense: given two…

We show that if $G$ and $H$ are finitely generated groups whose Hilbert compression exponent is positive, then so is the Hilbert compression exponent of the wreath $G \wr H$. We also prove an analogous result for coarse embeddings of wreath…

We get three types of results on measure equivalence rigidity; direct product groups of Ozawa's class $\mathcal{S}$ groups, wreath product groups and amalgamated free products. We prove measure equivalence factorization results on direct…

We investigate closure results for C-approximable groups, for certain classes C of groups with invariant length functions. In particular we prove, each time for certain (but not necessarily the same) classes C that (i) the direct product of…

A result of Farahat and Higman shows that there is a ``universal'' algebra, $\mathrm{FH}$, interpolating the centres of symmetric group algebras, $Z(\mathbb{Z}S_n)$. We explain that this algebra is isomorphic to $\mathcal{R} \otimes…

A wreath product is a method to construct an association scheme from two association schemes. We determine the automorphism group of a wreath product. We show a known result that a wreath product is Schurian if and only if both components…

Using the notion of isoclinism introduced by P. Hall for finite p-groups, we show that many important classes of finite p-groups have stable cohomology detected by abelian subgroups, see Theorem 4.4. Moreover, we show that the stable…