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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)
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)
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