Zobrazeno 1 - 10
of 36
pro vyhledávání: '"Bunina, Elena"'
Autor:
Bunina, Elena
In this paper, we prove that the endomorphism rings End A and End A' of periodic infinite Abelian groups A and A' are elementarily equivalent if and only if the endomorphism rings of their p-components are elementarily equivalent for all primes p. Ad
Externí odkaz:
http://arxiv.org/abs/2410.11098
Autor:
Bunina, Elena
In this paper we study (logical) types and isotypical equivalence of torsion free Abelian groups. We describe all possible types of elements and standard 2-tuples of elements in these groups and classify separable torsion free Abelian groups up to is
Externí odkaz:
http://arxiv.org/abs/2409.07728
Autor:
Bunina, Elena
In this paper we give invariants that characterize isotypically equivalent Abelian periodic groups. Also, we describe types of standart tuples of elements in these groups. As the particular case we prove that two Abelian $p$-groups with separable red
Externí odkaz:
http://arxiv.org/abs/2402.11261
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:
Bunina, Elena, Kunyavskii, Boris
We prove that every locally inner endomorphism of a Chevalley group (or its elementary subgroup) over a local ring with an irreducible root system of rank >1 (with 1/2 for the systems A_2, F_4, B_l, C_l and with 1/3 for the system G_2) is inner, so t
Externí odkaz:
http://arxiv.org/abs/2308.10076
Autor:
Bunina, Elena, Vladykina, Maria
In this paper we prove that every automorphism of a Chevalley group with the root system G_2 over a commutative ring R with 1/3, generated by all its invertible elements and the ideal 2R is a composition of ring and inner automorphisms.
Comment:
Comment:
Externí odkaz:
http://arxiv.org/abs/2307.12920
Autor:
Bunina, Elena
In this paper we prove that every automorphism of a Chevalley group (or its elementary subgroup) with root system of rank >1 over a commutative ring (with 1/2 for the systems A_2, F_4, B_l, C_l; with 1/2 and 1/3 for the system G_2) is standard, i.e.,
Externí odkaz:
http://arxiv.org/abs/2304.13447
In this paper we study the Diophantine problem in Chevalley groups $G_\pi (\Phi,R)$, where $\Phi$ is an indecomposable root system of rank $> 1$, $R$ is an arbitrary commutative ring with $1$. We establish a variant of double centralizer theorem for
Externí odkaz:
http://arxiv.org/abs/2304.06259
In this paper, we prove a criterion of elementary equivalence of stable linear groups over fields of characteristic two.
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/2301.05613
Autor:
Bunina, Elena
In this paper we prove that if $G(R)=G_\pi (\Phi,R)$ $(E(R)=E_{\pi}(\Phi, R))$ is an (elementary) Chevalley group of rank $> 1$, $R$ is a local ring (with $\frac{1}{2}$ for the root systems ${\mathbf A}_2, {\mathbf B}_l, {\mathbf C}_l, {\mathbf F}_4,
Externí odkaz:
http://arxiv.org/abs/2208.13623