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- Nikolai Vavilov, Eugene Plotkin, Typeset By, A M S-T
- 1994

This is the rst in a series of papers dedicated to the structure of Chevalley groups over commutative rings. The goal of this series is to systematically develop methods of calculations in Chevalley groups over rings, based on the use of their minimal modules. As an application we give new direct proofs for normality of the elementary subgroup, description… (More)

- Eugene Plotkin, Andrei Semenov, Nikolai Vavilov
- IJAC
- 1998

We depict the weight diagrams of basic and adjoint representations of complex simple Lie algebras/algebraic groups and describe some of their uses.

- Robert M. Guralnick, Eugene Plotkin, Aner Shalev
- IJAC
- 2007

In the paper we pose and discuss new Burnside-type problems, where the role of nilpo-tency is replaced by that of solvability.

- NIKOLAI GORDEEV, FRITZ GRUNEWALD, BORIS KUNYAVSKII, EUGENE PLOTKIN

We obtain the following characterization of the solv-able radical R(G) of any finite group G: R(G) coincides with the collection of g ∈ G such that for any 3 elements a 1 , a 2 , a 3 ∈ G the subgroup generated by the elements g, a i ga −1 i , i = 1, 2, 3, is solv-able. In particular, this means that a finite group G is solvable if and only if in each… (More)

- Elena Aladova, Eugene Plotkin, Tatjana L. Plotkin
- Mathematics in Computer Science
- 2013

The aim of this work is to study the notions of elementarily equivalent and isotypic knowledge bases. We prove that isotypic knowledge bases are informationally equivalent.

- Eugene Plotkin, Typeset By, A M S-T
- 1996

This paper is devoted to the study of the surjective stability of the K 1 {functor for Chevalley groups of type E 7. This is a particular case of the stability problem for Chevalley groups, which was posed by H. Bass. In the paper, surjective stability of the K 1 {functor is proved under natural conditions on the dimension of the maximal spectrum of a ring… (More)

- Fritz Grunewald, Boris Kunyavskii, Eugene Plotkin
- IJAC
- 2013

- Eugene Plotkin, Typeset By, A M S-T
- 2007

The paper is devoted to surjective stability of K 1 {functor for Chevalley groups of type E 7. This is a particular case of stability problem for Chevalley groups, which was posed by H.Bass. In the paper surjective stability of K 1 {functor is proved under natural conditions on dimension of maximal spectrum of a ring and, independently, under some special… (More)

We will show the Gauss decomposition with prescribed torus elements for a Kac-Moody group over a field in general case.