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pro vyhledávání: '"Gvozdevsky, Pavel"'
Autor:
Gvozdevsky, Pavel
Publikováno v:
Journal of Algebra, Vol 666 (2025), pages 82-93
We prove that the width of any word in a simply connected Chevalley group of rank at least 2 over the ring that is a localisation of the ring of integers in a number field is bounded by a constant that depends only on the root system and on the degre
Externí odkaz:
http://arxiv.org/abs/2401.02934
Autor:
Bunina, Elena, Gvozdevsky, Pavel
In this paper we consider Chevalley groups over commutative rings with~$1$, constructed by irreducible root systems of rank $>1$. We always suppose that for the systems $A_2, B_\ell, C_\ell, F_4, G_2$ our rings contain $1/2$ and for the system $G_2$
Externí odkaz:
http://arxiv.org/abs/2311.01954
Autor:
Gvozdevsky, Pavel
Publikováno v:
journal of Groups, complexity, cryptology, Volume 16, Issue 1 (May 14, 2024) gcc:13493
We obtain several results concerning the concept of isotypic structures. Namely we prove that any field of finite transcendence degree over a prime subfield is defined by types; then we construct isotypic but not isomorphic structures with countable
Externí odkaz:
http://arxiv.org/abs/2308.10812
Autor:
Gvozdevsky, Pavel
We prove that an element from the Chevalley group of type $E_6$ or $E_7$ over a polynomial ring with coefficients in a small-dimensional ring can be reduced to an element of certain proper subsystem subgroup by a bounded number of elementary root ele
Externí odkaz:
http://arxiv.org/abs/2305.17012
Autor:
Gvozdevsky, Pavel
Publikováno v:
Communications in algebra, Vol. 51.4 (2023), Pages 1581-1593
We give an estimate for the width of the congruence subgroup $\mathrm{SL}(n,O_S,I)$ in Tits--Vaserstein generators, where $O_S$ is a localisation of the ring of integers in a number field $K$. We assume that either $K$ has a real embedding, or the id
Externí odkaz:
http://arxiv.org/abs/2206.11101
Autor:
Semenov, Andrei V., Gvozdevsky, Pavel
In this paper, we study affine commutative algebraic monoid structures on affine spaces over an arbitrary field of characteristic zero. We obtain full classification of such structures on $\mathbb{A}_K^2$ and $\mathbb{A}_K^3$ and describe some genera
Externí odkaz:
http://arxiv.org/abs/2109.10845
Autor:
Gvozdevsky, Pavel
Publikováno v:
St. Petersburg Math. J., Vol 33.6 (2022) Pages 897-925
In the present paper, we practicaly complete the solution of the problem on the description of overgroups of the subsystem subgroup $E(\Delta,R)$ in the Chevalley group $G(\Phi,R)$ over the ring $R$, where $\Phi$ is a simply laced root system, and $\
Externí odkaz:
http://arxiv.org/abs/2107.01258
Autor:
Gvozdevsky, Pavel
The current paper is an addition to the previous paper by author, where the overgroup lattice of the elementary subsystem subgroup $E(\Delta,R)$ of the Chevalley group $G(\Phi,R)$ for a large enough root subsystem $\Delta$ was studied. Now we study t
Externí odkaz:
http://arxiv.org/abs/2107.01249
Autor:
Gvozdevsky, Pavel
Publikováno v:
Journal of Algebra, Vol. 602 (2022) Pages 300-321
We prove that a matrix from the split orthogonal group over a polynomial ring with coefficients in a small-dimensional ring can be reduced to a smaller matrix by a bounded number of elementary orthogonal transformations. The bound is given explicitly
Externí odkaz:
http://arxiv.org/abs/2106.12697