Related papers: Subgroup induction property for branch groups

For a finite simplicial graph $\Gamma$, let $G(\Gamma)$ denote the right-angled Artin group on the complement graph of $\Gamma$. In this article, we introduce the notions of "induced path lifting property" and "semi-induced path lifting…

We prove that every free group G with infinitely many generators admits a Hausdorff group topology T with the following property: for every T-open neighbourhood U of the identity of G, each element g in G can be represented as a product…

We study actions of finitely generated groups on $\bbR$-trees under some stability hypotheses. We prove that either the group splits over some controlled subgroup (fixing an arc in particular), or the action can be obtained by gluing…

We prove an accessibility theorem for finite-index splittings of groups. Given a finitely presented group G there is a number n(G) such that, for every reduced locally finite G-tree T with finitely generated stabilizers, T/G has at most…

Trees without vertices of degree $2$ are sometimes named topological trees. In this work, we bring forward the study of the inducibility of (rooted) topological trees with a given number of leaves. The inducibility of a topological tree $S$…

The property that the polynomial cohomology with coefficients of a finitely generated discrete group is canonically isomorphic to the group cohomology is called the (weak) isocohomological property for the group. In the case when a group is…

Let $G=G_1 \ast \ldots \ast G_k \ast F_N$ be a free product of finitely presented groups, where $F_N$ is a free group of rank $N \in \mathbb{N}$. Let $\mathrm{Out}(G,\mathcal{G})$ be the subgroup of $\mathrm{Out}(G)$ preserving the set of…

Let $G$ be a reductive algebraic group scheme defined over ${\mathbb F}_{p}$ and $k$ be an algebraically closed field of characteristic $p$. There are two associated families of finite group schemes, the $r$-th Frobenius kernels, denoted by…

We prove that a saturated weakly branch group $G$ has the property $R_\infty$ (any automorphism $\phi:G\to G$ has infinite Reidemeister number) in each of the following cases: 1) any element of $Out(G)$ has finite order; 2) for any $\phi$…

We give a complete criterion for when two hyperbolic automorphisms of a tree generate a free, discrete subgroup. The decision depends only on three geometric invariants: the translation lengths of the generators and the length of overlap of…

An extremal property of finite Schur sigma-groups G is described in terms of their path to the root in the descendant tree of their abelianization G/G'. The phenomenon is illustrated and verified by all known examples of Galois groups…

We say that a finite group $G$ satisfies the independence property if, for every pair of distinct elements $x$ and $y$ of $G$, either $\{x,y\}$ is contained in a minimal generating set for $G$ or one of $x$ and $y$ is a power of the other.…

There are a variety of ways to associate directed or undirected graphs to a group. It may be interesting to investigate the relations between the structure of these graphs and characterizing certain properties of the group in terms of some…

For a family of group words $w$ we show that if $G$ is a profinite group in which all $w$-values are contained in a union of finitely many subgroups with a prescribed property, then $w(G)$ has the same property as well. In particular, we…

To a finite group G one can associate a tower of wreath products S_n[G]. It is well known that the graded direct sum of the Grothendieck groups of the categories of finite dimensional complex representations of these groups can be given the…

A maximum sequence $S$ of vertices in a graph $G$, so that every vertex in $S$ has a neighbor which is independent, or is itself independent, from all previous vertices in $S$, is called a Grundy dominating sequence. The Grundy domination…

We introduce shortcut graphs and groups. Shortcut graphs are graphs in which cycles cannot embed without metric distortion. Shortcut groups are groups which act properly and cocompactly on shortcut graphs. These notions unify a surprisingly…

The aim of this paper is to use the framework of incidence geometry to develop a theory that permits to model both the inner and outer automorphisms of a group G simultaneously. More precisely, to any group G, we attempt to associate an…

We present several applications of the weak specification property and certain topological Markov properties, recently introduced by S. Barbieri, F. Garc\'{i}a-Ramos and H. Li, and implied by the pseudo-orbit tracing property, for general…

This paper studies properties of entropy functions that are induced by groups and subgroups. We showed that many information theoretic properties of those group induced entropy functions also have corresponding group theoretic…