Zobrazeno 1 - 10
of 114
pro vyhledávání: '"Olshanskii, A. Yu."'
We construct novel examples of finitely generated groups that exhibit seemingly-contradicting probabilistic behaviors with respect to Burnside laws. We construct a finitely generated group that satisfies a Burnside law, namely a law of the form $x^n=
Externí odkaz:
http://arxiv.org/abs/2409.09630
Publikováno v:
Journal of Algebra and Its Applications, 22:09 (2023), 2350188
We show, in particular, that, if a finite group $H$ is a retract of any finite group containing $H$ as a verbally closed subgroup, then the centre of $H$ is a direct factor of $H$.
Comment: 13 pages. A Russian version of this paper is at http://
Comment: 13 pages. A Russian version of this paper is at http://
Externí odkaz:
http://arxiv.org/abs/2109.12397
Autor:
Olshanskii, A. Yu., Sapir, M. V.
We construct and study finitely presented groups with quadratic Dehn function (QD-groups) and present the following applications of the method developed in our recent papers. (1) The isomorphism problem is undecidable in the class of QD-groups. (2) F
Externí odkaz:
http://arxiv.org/abs/2012.10417
We construct a finitely presented group with quadratic Dehn function and undecidable conjugacy problem. This solves E. Rips' problem formulated in 1992. v2: misprints corrected. v3: lemmas 4.7, 4.10 corrected, more misprints fixed.
Comment: 83 p
Comment: 83 p
Externí odkaz:
http://arxiv.org/abs/1809.00280
Autor:
Olshanskii, A. Yu
On the one hand, it is well known that the only subquadratic Dehn function of finitely presented groups is the linear one. On the other hand there is a huge class of Dehn functions $d(n)$ with growth at least $n^4$ (essentially all possible such Dehn
Externí odkaz:
http://arxiv.org/abs/1710.00550
Autor:
Olshanskii, A. Yu., Sapir, M. V.
We prove that for every $r>0$ if a non-positively curved $(p,q)$-map $M$ contains no flat submaps of radius $r$, then the area of $M$ does not exceed $Crn$ for some constant $C$. This strengthens a theorem of Ivanov and Schupp. We show that an infini
Externí odkaz:
http://arxiv.org/abs/1702.08205
Autor:
Olshanskii, A. Yu.
In this note, we consider a 'thrifty' version of Kaluzhnin - Krasner's embedding in wreath products and apply it to extensions by finite groups and to metabelian groups.
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/1502.07052
Autor:
Olshanskii, Alexander Yu.
An embedding construction $G\hookrightarrow H$ for groups $G$ with a length function was introduced by the author earlier. Here we obtain new properties of this embedding, answering some questions raised by M.V. Sapir. In particular, an analog of Tit
Externí odkaz:
http://arxiv.org/abs/1406.0336
Autor:
Olshanskii, A. Yu., Osin, D. V.
We construct first examples of non-trivial groups without non-cyclic free subgroups whose reduced $C^\ast$-algebra is simple and has unique trace. This answers a question of de la Harpe. Both torsion and torsion free examples are provided. In particu
Externí odkaz:
http://arxiv.org/abs/1401.7300
Autor:
Olshanskii, A. Yu.
We prove that for arbitrary two finitely generated subgroups A and B having infinite index in a free group F, there is a subgroup H of finite index in B such that the subgroup generated by A and H has infinite index in F. The main corollary of this t
Externí odkaz:
http://arxiv.org/abs/1308.3192