Related papers: Wreath product of groups with infinite conjugacy c…
We characterise the simplicity of metric ultraproducts of a family of metric groups. We also present several new examples of simple groups, such as metric ultraproducts of finite and infinite symmetric groups, linear groups, and interval…
We construct finitely generated groups with strong fixed point properties. Let $\mathcal{X}_{ac}$ be the class of Hausdorff spaces of finite covering dimension which are mod-$p$ acyclic for at least one prime $p$. We produce the first…
Let $G$ be a closed highly homogeneous subgroup of $S_{\infty}$ not involving circular orderings. We show that the closure of a conjugacy class from $G$ contains a conjugacy class which is comeagre in it. Furthermore, we show that the…
We study the conjugacy classes of the classical affine groups. We derive generating functions for the number of classes analogous to formulas of Wall and the authors for the classical groups. We use these to get good upper bounds for the…
Given a quasi-monomial, respectively an almost monomial, group $A$ and a cyclic group $C$ of prime order $p>0$, we show that the wreath product $W=A\wr C$ is quasi-monomial (respectively almost monomial), if certain technical conditions…
In recent years, knapsack problems for (in general non-commutative) groups have attracted attention. In this paper, the knapsack problem for wreath products is studied. It turns out that decidability of knapsack is not preserved under…
A permutation group is innately transitive if it has a transitive minimal normal subgroup, and this subgroup is called a plinth. In this paper we study three special types of inclusions of innately transitive permutation groups in wreath…
Let G be a finite group. A complete system of pairwise orthogonal idempotents is constructed for the wreath product of G by the symmetric group by means of a fusion procedure, that is by consecutive evaluations of a rational function with…
In \cite{CDD22} we investigated the structure of $\ast$-isomorphisms between von Neumann algebras $L(\Gamma)$ associated with graph product groups $\Gamma$ of flower-shaped graphs and property (T) wreath-like product vertex groups as in…
For any finite group Q not of prime power order, we construct a group G that is virtually of type F, contains infinitely many conjugacy classes of subgroups isomorphic to Q, and contains only finitely many conjugacy classes of other finite…
We review some recent results on properties of tensor product and fusion coefficients under complex conjugation of one of the factors. Some of these results have been proven, some others are conjectures awaiting a proof, one of them…
We present generating functions for extensions of multiplicative invariants of wreath symmetric products of orbifolds presented as the quotient by the locally free action of a compact, connected Lie group in terms of orbifold sector…
There are several graphs defined on groups. Among them we consider graphs whose vertex set consists conjugacy classes of a group $G$ and adjacency is defined by properties of the elements of conjugacy classes. In particular, we consider…
In this paper, we showed how a group acting regularly and a diagonal group are embedded into the wreath products in there product action using the Cartesian Decomposition.
A combinatorial summation identity over the lattice of labelled hypertrees is established that allows one to gain concrete information on the Euler characteristics of various automorphism groups of free products of groups.
All possible products of all elements of an odd order finite group are considered. A set of all such products is called as a K-set. A hypothesis of K-set coincidence of any group of an odd order with its commutant is proposed and the…
We show that the conjugacy problem in a wreath product $A \wr B$ is uniform-$\mathsf{TC}^0$-Turing-reducible to the conjugacy problem in the factors $A$ and $B$ and the power problem in $B$. If $B$ is torsion free, the power problem for $B$…
It is shown that there exists a finitely generated infinite simple group of infinite commutator width, and that the commutator width of a finitely generated infinite boundedly simple group can be arbitrarily large. Besides, such groups can…
We developed computer algebra tools for enumerating conjugacy classes of independent subsets and generating sets of symmetric groups up to $n=7$, and carried out an initial analysis of the obtained results.
Let $\mathbf{G}$ be a unipotent group scheme defined in terms of a nilpotent Lie lattice over the ring $\mathcal{O}$ of integers of a number field. We consider bivariate zeta functions of groups of the form $\mathbf{G}(\mathcal{O})$…