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pro vyhledávání: '"Guba, Victor"'
Autor:
Guba, Victor
Publikováno v:
journal of Groups, complexity, cryptology, Volume 15, Issue 1 (October 19, 2023) gcc:11315
This is a survey of our recent results on the amenability problem for Thompson's group $F$. They mostly concern esimating the density of finite subgraphs in Cayley graphs of $F$ for various systems of generators, and also equations in the group ring
Externí odkaz:
http://arxiv.org/abs/2305.07113
Autor:
Guba, Victor
A (discrete) group is called amenable whenever there exists a finitely additive right invariant probablity measure on it. For Thompson's group $F$ the problem whether it is amenable is a long-standing open question. We consider presentation of $F$ in
Externí odkaz:
http://arxiv.org/abs/2304.04322
Autor:
Guba, Victor
We improve some known estimates for the density of the Cayley graph of Thompson's group F in standard generators.
Comment: arXiv admin note: text overlap with arXiv:2112.09812
Comment: arXiv admin note: text overlap with arXiv:2112.09812
Externí odkaz:
http://arxiv.org/abs/2210.12304
Autor:
Guba, Victor
Let $R=K[G]$ be a group ring of a group $G$ over a field $K$. It is known that if $G$ is amenable then $R$ satisfies the Ore condition: for any $a,b\in R$ there exist $u,v\in R$ such that $au=bv$, where $u\ne0$ or $v\ne0$. It is also true for amenabl
Externí odkaz:
http://arxiv.org/abs/2201.02308
Autor:
Guba, Victor
In this paper we introduce a concept of an evacuation scheme on the Cayley graph of an infinite finitely generated group. This is a collection of infinite simple paths bringing all vertices to infinity. We impose a restriction that every edge can be
Externí odkaz:
http://arxiv.org/abs/2112.09812
Autor:
Guba, Victor
Let $R=K[G]$ be a group ring of a group $G$ over a field $K$. The Ore condition says that for any $a,b\in R$ there exist $u,v\in R$ such that $au=bv$, where $u\ne0$ or $v\ne0$. It always holds whenever $G$ is amenable. Recently it was shown that for
Externí odkaz:
http://arxiv.org/abs/2101.01848
Autor:
Guba, Victor
Let $M$ be a cancellative monoid. It is known~\cite{Ta54} that if $M$ is left amenable then the monoid ring $K[M]$ satisfies Ore condition, that is, there exist nontrivial common right multiples for the elements of this ring. In~\cite{Don10} Donnelly
Externí odkaz:
http://arxiv.org/abs/2101.00344
Autor:
Guba, Victor
By the density of a finite graph we mean its average vertex degree. For an $m$-generated group, the density of its Cayley graph in a given set of generators, is the supremum of densities taken over all its finite subgraphs. It is known that a group w
Externí odkaz:
http://arxiv.org/abs/1909.01882
Autor:
Guba, Victor
We answer the question by Matt Brin on the structure of diagram groups over semigroup presentation ${\mathcal P}=\langle a,b,c\mid a=bc,b=ca,c=ab\rangle$. In the talk on Oberwolfach workshop, Brin conjectured that the diagram group over $\mathcal P$
Externí odkaz:
http://arxiv.org/abs/1909.01877
Autor:
Guba, Victor, Sapir, Mark
To every finitely generated group one can assign the conjugacy growth function that counts the number of conjugacy classes intersecting a ball of radius $n$. Results of Ivanov and Osin show that the conjugacy growth function may be constant even if t
Externí odkaz:
http://arxiv.org/abs/1003.1293