Zobrazeno 1 - 10
of 72
pro vyhledávání: '"Vavilov, Nikolai"'
In this paper we establish a definitive result which almost completely closes the problem of bounded elementary generation for Chevalley groups of rank $\ge 2$ over arbitrary Dedekind rings $R$ of arithmetic type, with uniform bounds. Namely, we show
Externí odkaz:
http://arxiv.org/abs/2307.15756
The main result of the present paper is bounded elementary generation of the Steinberg groups $\mathrm{St}(\Phi,R)$ for simply laced root systems $\Phi$ of rank $\ge 2$ and arbitrary Dedekind rings of arithmetic type. Also, we prove bounded generatio
Externí odkaz:
http://arxiv.org/abs/2307.05526
We prove that Chevalley groups over polynomial rings $\mathbb F_q[t]$ and over Laurent polynomial $\mathbb F_q[t,t^{-1}]$ rings, where $\mathbb F_q$ is a finite field, are boundedly elementarily generated. Using this we produce explicit bounds of the
Externí odkaz:
http://arxiv.org/abs/2204.10951
Autor:
Vavilov, Nikolai, Zhang, Zuhong
Let $R$ be an associative ring with 1, $G=GL(n, R)$ be the general linear group of degree $n\ge 3$ over $R$. In this paper we calculate the relative centralisers of the relative elementary subgroups or the principal congruence subgroups, correspondin
Externí odkaz:
http://arxiv.org/abs/2004.14285
Autor:
Vavilov, Nikolai, Zhang, Zuhong
Let $R$ be any associative ring with $1$, $n\ge 3$, and let $A,B$ be two-sided ideals of $R$. In our previous joint works with Roozbeh Hazrat [17,15] we have found a generating set for the mixed commutator subgroup $[E(n,R,A),E(n,R,B)]$. Later in [29
Externí odkaz:
http://arxiv.org/abs/2004.12870
Autor:
Vavilov, Nikolai, Zhang, Zuhong
In the present paper we find generators of the mixed commutator subgroups of relative elementary groups and obtain unrelativised versions of commutator formulas in the setting of Bak's unitary groups. It is a direct sequel of our similar results were
Externí odkaz:
http://arxiv.org/abs/2004.00576
Autor:
Vavilov, Nikolai, Zhang, Zuhong
In the present paper, which is a direct sequel of our papers [10,11,35] joint with Roozbeh Hazrat, we achieve a further dramatic reduction of the generating sets for commutators of relative elementary subgroups in Chevalley groups. Namely, let $\Phi$
Externí odkaz:
http://arxiv.org/abs/2003.07230
Autor:
Vavilov, Nikolai, Zhang, Zuhong
In the present paper we continue the study of the elementary commutator subgroups $[E(n,A),E(n,B)]$, where $A$ and $B$ are two-sided ideals of an associative ring $R$, $n\ge 3$. First, we refine and expand a number of the auxiliary results, both clas
Externí odkaz:
http://arxiv.org/abs/1911.10526
Autor:
Vavilov, Nikolai, Zhang, Zuhong
In our previous joint papers with Roozbeh Hazrat and Alexei Stepanov we established commutator formulas for relative elementary subgroups in $GL(n,R)$, $n\ge 3$, and other similar groups, such as Bak's unitary groups, or Chevalley groups. In particul
Externí odkaz:
http://arxiv.org/abs/1910.14444
Autor:
Vavilov, Nikolai, Zhang, Zuhong
Let $R$ be any associative ring with $1$, $n\ge 3$, and let $A,B$ be two-sided ideals of $R$. In the present paper we show that the mixed commutator subgroup $[E(n,R,A),E(n,R,B)]$ is generated as a group by the elements of the two following forms: 1)
Externí odkaz:
http://arxiv.org/abs/1910.08984