Eugene Plotkin

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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)
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)
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)