Related papers: When Schrier transversals grow wild

A generalized Baumslag-Solitar (GBS) group is a finitely generated group acting on a tree with infinite cyclic edge and vertex stabilizers. We show how to determine effectively the rank (minimal cardinality of a generating set) of a GBS…

A subgroup of a group is contranormal if its normal closure coincides with the group. We call such groups without proper contranormal subgroups contranormal-free. In this paper we prove various results concerning contranormal-free groups…

A subgroup $H$ of a free group $F$ is called inert in $F$ if for every $G < F$ the rank of the intersection of $H$ with $G$ is no grater than the rank of $G$. In this paper we expand the known families of inert subgroups. We show that the…

We show that the (topological) full group of a minimal pseudogroup over the Cantor set satisfies various rigidity phenomena of topological dynamical and combinatorial nature. Our main result applies to its possible homomorphisms into other…

Given a Kaehler group $G$ and a primitive class $\phi \in H^1(G;Z)$, we show that the rank gradient of $(G;\phi)$ is zero if and only if Ker $\phi$ is finitely generated. Using this approach, we give a quick proof of the fact (originally…

A topological group $G$ is topologically normally generated if there exists $g \in G$ such that the normal closure of $g$ is dense in $G$. Let $S$ be a tame, infinite type surface whose mapping class group $\mathrm{Map}(S)$ is generated by…

We study the finitely generated Hausdorff spectrum of spinal automorphism groups acting on rooted trees. Given any $\alpha \in [0,1]$, we construct a branch group $G_\alpha$ such that $G_\alpha$ has a finitely generated subgroup $H$ where…

We give an example of a subgroup of SL(2,C) which is a strictly ascending HNN extension of a non-abelian finitely generated free group F. In particular, we exhibit a free group F in SL(2,C) of rank 6 which is conjugate to a proper subgroup…

In this paper, we are concerned with mean hitting time $\langle\mathcal{H}\rangle$ for random walks on recursive growth tree networks that are built based on an arbitrary tree as the seed via implementing various primitive graphic…

To any finite graph $X$ (viewed as a topological space) we assosiate some explicit compact metric space ${\cal X}^r(X)$ which we call {\it the reflection tree of graphs $X$}. This space is of topological dimension $\le1$ and its connected…

In this article we investigate the L^1-norm of certain functions on groups called divisibility functions. Using these functions, their connection to residual finiteness, and integration theory on profinite groups, we define the residual…

We show that certain classes of graphs of free groups contain surface subgroups, including groups with positive $b_2$ obtained by doubling free groups along collections of subgroups, and groups obtained by "random" ascending HNN extensions…

If $G$ is a finitely generated group and $X$ a $G$-set, the growth of the action of $G$ on $X$ is the function that measures the largest cardinality of a ball of radius $n$ in the Schreier graph $\Gamma(G,X)$. In this note we consider the…

It is shown that for a normal subgroup $N$ of a group $G$, $G/N$ cyclic, the kernel of the map $N^{\mathrm{ab}}\to G^{\mathrm{ab}}$ satisfies the classical Hilbert 90 property (cf. Thm. A). As a consequence, if $G$ is finitely generated,…

Let $G$ be a group. The intersection graph of subgroups of $G$, denoted by $\mathscr{I}(G)$, is a graph with all the proper subgroups of $G$ as its vertices and two distinct vertices in $\mathscr{I}(G)$ are adjacent if and only if the…

Let $\frak{F}$ be a class of finite groups. A subgroup $H$ of a finite group $G$ is said to be $\mathfrak{F_{\mathrm s}}$-quasinormal in $G$ if there exists a normal subgroup $T$ of $G$ such that $HT$ is $s$-permutable in $G$ and $(H\cap…

For a finite group $G$, we define the inclusion graph of subgroups of $G$, denoted by $\mathcal I(G)$, is a graph having all the proper subgroups of $G$ as its vertices and two distinct vertices $H$ and $K$ in $\mathcal I(G)$ are adjacent…

It is known that every infinite index quasi-convex subgroup $H$ of a non-elementary hyperbolic group $G$ is a free factor in a larger quasi-convex subgroup of $G$. We give a probabilistic generalization of this result. That is, we show that…

We introduce a framework for constructing fractal trees via analytic generator fields, replacing discrete affine transformations and symbolic rewriting rules by the integration of smooth vector fields in an internal state space. In this…

Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…