Zobrazeno 1 - 10
of 109
pro vyhledávání: '"Fel'shtyn, Alexander"'
We prove a dichotomy between rationality and a natural boundary for the analytic behavior of the Reidemeister zeta function for automorphisms of non-finitely generated torsion abelian groups and for endomorphisms of groups $\mathbb Z_p^d,$ where $\ma
Externí odkaz:
http://arxiv.org/abs/2202.09776
We consider coincidence Reidemeister zeta functions for tame endomorphism pairs of nilpotent groups of finite rank, shedding new light on the subject by means of profinite completion techniques. In particular, we provide a closed formula for coincide
Externí odkaz:
http://arxiv.org/abs/2102.10900
Autor:
Fel'shtyn, Alexander, Zietek, Malwina
In this paper we continue to study the Reidemeister zeta function. We prove P\'olya -- Carlson dichotomy between rationality and a natural boundary for analytic behavior of the Reidemeister zeta function for a large class of automorphisms of Abelian
Externí odkaz:
http://arxiv.org/abs/1906.09959
We introduce new zeta functions related to an endomorphism $\phi$ of a discrete group $\Gamma$. They are of two types: counting numbers of fixed ($\rho\sim \rho\circ\phi^n$) irreducible representations for iterations of $\phi$ from an appropriate dua
Externí odkaz:
http://arxiv.org/abs/1804.02874
Publikováno v:
In Indagationes Mathematicae July 2022 33(4):753-767
Let $R(\phi)$ be the number of $\phi$-conjugacy (or Reidemeister) classes of an endomorphism $\phi$ of a group $G$. We prove for several classes of groups (including polycyclic) that the number $R(\phi)$ is equal to the number of fixed points of the
Externí odkaz:
http://arxiv.org/abs/1704.09013
In the paper we study twisted conjugacy classes and isogredience classes for automorphisms of reductive linear algebraic groups. We show that reductive linear algebraic groups over some fields of zero characteristic possess the $R_\infty$ and $S_\inf
Externí odkaz:
http://arxiv.org/abs/1506.02464
Autor:
Fel'shtyn, Alexander, Lee, Jong Bum
Publikováno v:
Contemporary Mathematics, vol. 669, 77-103, 2016
We develop the Reidemeister theory of iterations of a group endomorphism $\varphi$ and study the asymptotic behavior of the sequence of the Reidemeister numbers of iterations $\{R(\varphi^k)\}$, the essential periodic $[\varphi]$-orbits and the heigh
Externí odkaz:
http://arxiv.org/abs/1412.4524
We prove that the growth rate of an endomorphism of a finitely generated nilpotent group equals to the growth rate of induced endomorphism on its abelinization, generalizing the corresponding result for an automorphism in [14]. We also study growth r
Externí odkaz:
http://arxiv.org/abs/1411.6360
Autor:
Fel'shtyn, Alexander, Lee, Jong Bum
We study the asymptotic behavior of the sequence of the Nielsen numbers $\{N(f^k)\}$, the essential periodic orbits of $f$ and the homotopy minimal periods of $f$ by using the Nielsen theory of maps $f$ on infra-solvmanifolds of type $R$. We give a l
Externí odkaz:
http://arxiv.org/abs/1403.7631