Related papers: Subgroup of interval exchanges generated by torsio…

Distributive subsets of the group of all invertible continuous binary operations on a topological space are considered, and it is proved that the subgroups generated by them are also distributive. A criterion for the distributivity of a…

For a nonorientable surface, the twist subgroup is an index 2 subgroup of the mapping class group. It is generated by Dehn twists about two-sided simple closed curves. In this paper, we study involution generators of the twist subgroup. We…

We systematize and analyze some results obtained in Subset Combinatorics of $G$ groups after publications the previous surveys [1-4]. The main topics: the dynamical and descriptive characterizations of subsets of a group relatively their…

We show that every effectively closed action of a finitely generated group $G$ on a closed subset of $\{0,1\}^{\mathbb{N}}$ can be obtained as a topological factor of the $G$-subaction of a $(G \times H_1 \times H_2)$-subshift of finite…

Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated quantum many-particle systems. For the simplest spinless fermion (or boson) systems with say $m$ fermions (or bosons) in $N$ single…

We study the intersection lattice of the arrangement $\mathcal{A}^G$ of subspaces fixed by subgroups of a finite linear group $G$. When $G$ is a reflection group, this arrangement is precisely the hyperplane reflection arrangement of $G$.…

For a finite group $G$, $G$-transfer systems are combinatorial objects which encode the homotopy category of $G$-$N_\infty$ operads, whose algebras in $G$-spectra are $E_\infty$ $G$-spectra with a specified collection of multiplicative…

Let $G=(V,A)$ be a digraph. For $X\subseteq V$, the subdigraph of $G$ induced by $X$ is denoted by $G[X]$. A subset $I$ of $V$ is an interval of $G$ if for every $a,b \in I$ and $x \in V \setminus I$, $(x,a) \in A$ if and only if $(x,b) \in…

Let $G$ be a group. The orbits of the natural action of $\Aut(G)$ on $G$ are called "automorphism orbits" of $G$, and the number of automorphism orbits of $G$ is denoted by $\omega(G)$. Let $G$ be a virtually nilpotent group such that…

A natural generalization of interval exchange maps are linear involutions, first introduced by Danthony and Nogueira. Recurrent train tracks with a single switch provide a subclass of linear involutions. We call such linear involutions…

We consider the class of finitely generated groups whose relators are powers of commutators of the generators. This class contains as a small subclass graph groups (also called RAAGs), namely if all powers are one. Graph groups are the only…

Let $V$ be a standard subspace in the complex Hilbert space $H$ and $G$ be a finite dimensional Lie group of unitary and antiunitary operators on $H$ containing the modular group $(\Delta_V^{it})_{t \in R}$ of $V$ and the corresponding…

Let $K$ be a field and $G$ be a group of its automorphisms. If $G$ is precompact then $K$ is a generator of the category of smooth (i.e. with open stabilizers) $K$-semilinear representations of $G$. There are non-semisimple smooth…

Let $X = G/\Gamma$ be a quotient of a real Lie group by a non-uniform lattice. Consider a one-parameter subgroup $F$ of $G$ that is $\operatorname{Ad}$-diagonalizable over $\mathbb{C}$ and whose action on $(X,m_X)$ is mixing. In this…

We construct Grothendieck pairs witnessing that the following are not profinite invariants: stable commutator length, quasimorphisms (answering a question of Echtler and Kammeyer), property NL (which obstructs actions on hyperbolic spaces),…

A group $G$ is invariably generated if there exists a subset $S \subseteq G$ such that, for every choice $g_s \in G$ for $s \in S$, the group $G$ is generated by $\{ s^{g_s} \mid s \in S \}$. In [GGJ16] Gelander, Golan and Juschenko showed…

Let $G$ be a multiplicatively written finite group. We denote by $\mathsf E(G)$ the smallest integer $t$ such that every sequence of $t$ elements in $G$ contains a product-one subsequence of length $|G|$. In 1961, Erd\H{o}s, Ginzburg and…

Let n >1 be an integer, and G a doubly transitive subgroup of the symmetric group on X={1,...,n}. In this paper we find all linear group representations rho of G on an euclidean vector space V which contains a set of equiangular vector…

For a simple real Lie group $G$ with Heisenberg parabolic subgroup $P$, we study the corresponding degenerate principal series representations. For a certain induction parameter the kernel of the conformally invariant system of second order…

Let $G$ be a connected reductive algebraic group defined over a non-archimedean locally compact field $F$ of odd residue characteristic. Let $\theta$ be an $F$-rational involution of $G$ and $H$ be the reductive $F$-group $G^\theta$. We…