相关论文: Uniform Exponential Growth of Polycyclic Groups

We show that a relatively hyperbolic group either is virtually cyclic or has uniform exponential growth.

We show that the mapping class group of an orientable finite type surface has uniformly exponential growth, as well as various closely related groups. This provides further evidence that mapping class groups may be linear.

We announce the folowing result: Any finitely generated non virtually solvable linear group over a field of characteristic zero has uniform exponential growth.

This paper studies the locally uniform exponential growth and product set growth for a finitely generated group $G$ acting properly on a finite product of hyperbolic spaces. Under the assumption of coarsely dense orbits or shadowing…

We prove the following version of Milnor's theorem on solvable groups of exponential growth: A finitely generated solvable group which is not polycyclic contains an ascending HNN extension. Consequently, a finitely generated solvable group…

We give several sufficient conditions for uniform exponential growth in the setting of virtually torsion-free hierarchically hyperbolic groups. For example, any hierarchically hyperbolic group that is also acylindrically hyperbolic has…

We show that finitely generated groups with a polynomial dimension growth have Yu's property A and give an example of such groups.

We prove that all groups of exponential growth support non-constant positive harmonic functions. In fact, out results hold in the more general case of strongly connected, finitely supported Markov chains invariant under some transitive…

In this paper, we consider the conjugacy growth function of a group, which counts the number of conjugacy classes which intersect a ball of radius $n$ centered at the identity. We prove that in the case of virtually polycyclic groups, this…

Using a theorem of J. Groves we give a ping-pong proof of Osin's uniform exponential growth for solvable groups. We discuss slow exponential growth and show that this phenomenon disappears as one passes to a finite index subgroup.

We present a survey of results related to the Milnor's problem on group growth. We discuss the cases of polynomial growth, exponential but not uniformly exponential growth, but the main part of the article is devoted to the intermediate…

Let Mod(S) denote the mapping class group of a compact, orientable surface S. We prove that finitely generated subgroups of Mod(S) which are not virtually abelian have uniform exponential growth with minimal growth rate bounded below by a…

This note records some observations concerning geodesic growth functions. If a nilpotent group is not virtually cyclic then it has exponential geodesic growth with respect to all finite generating sets. On the other hand, if a finitely…

We use actions on trees to determine uniform exponential growth for subgroups of $GL_2$.

We investigate the conjugacy growth of finitely generated linear groups. We show that finitely generated non-virtually-solvable subgroups of GL_d have uniform exponential conjugacy growth and in fact that the number of distinct polynomials…

We strengthen the maximal ergodic theorem for actions of groups of polynomial growth to a form involving jump quantity, which is the sharpest result among the family of variational or maximal ergodic theorems. As a consequence, we deduce in…

We provide the first example of a finitely presented, and the first example of a simple, group of non-uniform exponential growth. The example is given by Thompson's group V.

This note constructs a finitely generated group $W$ whose word-growth is exponential, but for which the infimum of the growth rates over all finite generating sets is 1 -- in other words, of non-uniformly exponential growth. This answers a…

We prove that every polycyclic group of nonlinear growth admits a strongly aperiodic SFT and has an undecidable domino problem. This answers a question of [4] and generalizes the result of [2].

Iterated monodromy groups of postcritically-finite rational maps form a rich class of self-similar groups with interesting properties. There are examples of such groups that have intermediate growth, as well as examples that have…