Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · math/0101010

Reidemeister number of any automorphism of a Gromov hyperbolic group is infinite

Alexander Fel'shtyn
View original source ↗Read source document ↗Export metadata ↓

Abstract

We show that the number of twisted conjugacy classes is infinite for any automorphism of non-elementary, Gromov hyperbolic group . An analog of Selberg theory for twisted conjugacy classes is proposed.

Explore related subjects

math.GRmath.ATmath.DG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Alexander Fel'shtyn. 2001-01-01. Reidemeister number of any automorphism of a Gromov hyperbolic group is infinite. https://arxiv.org/abs/math/0101010

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Finiteness conditions on skew braces and solutions of the Yang-Baxter equation

A finite non-degenerate set-theoretic solution $(X,r)$ of the Yang-Baxter equation gives rise to a structure skew brace $B(X,r)$ that is a $λ_f$-skew brace, i.e. every element has finitely many $λ$-images, and whose additive group is $FC$. This motivates the study of finiteness conditions on skew braces. We first study the general class of $λ_f$ skew braces and the subclass where the additive group is $FC$, showing that these properties share a resemblance to finite conjugacy, having an analog of the $FC$-center and several analogous structural results. Furthermore, by passing through the structure skew brace of a solution, this property measures whether elements are contained in a finite decomposition factor, identifying a class of infinite solutions that may exhibit similar properties to finite ones. Finally, we show that for a sub skew brace where both groups have finite index, both indices need to coincide and that such a sub skew brace contains a strong left ideal of finite index.

math.GR↗
arXiv2026

Non-uniform exponential growth and the decay of growth rates in growing dimensions

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 $V$. Our methods also show that the infimal exponential growth rates of $\mathrm{Aut}(F_{2^{n+2}})$ and of $\mathrm{EL}_{2^{n+2}}(R)$, for every finitely generated ring $R$, tend to $1$. As an application, we obtain the first example of an acylindrically hyperbolic group, and the first example of a Kazhdan group, of non-uniform exponential growth.

math.GR↗
arXiv2026

Solvable Supplements to Normalizers of Cyclic 2-Subgroups

Amberg and Kazarin proved that a finite group is solvable if the normalizer of every cyclic subgroup of prime power order has a solvable supplement. We substantially relax this hypothesis by requiring it only for cyclic $2$-subgroups. This condition, denoted by $\mathrm{SSN}_2$, sharply restricts the nonabelian composition factors of the group to the family $\PSL_2(q)$, where $q\geq7$ is a prime power satisfying $q\equiv3\pmod4$. Conversely, this family is precisely the nonabelian finite simple groups that satisfy $\mathrm{SSN}_2$. Consequently, a finite group satisfying $\mathrm{SSN}_2$ is solvable if and only if it has no section isomorphic to one of these groups.

math.GR↗