30 citations · 75 across the 12 of their papers we have counts for
17 papers
Solvability of unimodular equations in groups and Lie algebras
Anton A. Klyachko, Mikhail A. Mikheenko, Alexander Yu. Olshanskii
Our results implies, in particular, that a finitely generated solvable group is nilpotent if and only if it contains a solution to any unimodular equation, i.e., an equation of…
Locally finite varieties of nonassociative algebras
Yuri Bahturin, Alexander Olshanskii
We study locally finite varieties (=primitive classes) of linear algebras over finite fields. We do not assume that our algebras are associative or Lie. We are interested in the ba…
Asymptotic Burnside laws
Gil Goffer, Be'eri Greenfeld, Alexander Yu. Olshanskii
We construct novel examples of finitely generated groups that exhibit seemingly-contradicting probabilistic behaviors with respect to Burnside laws. We construct a finitely generat…
On generic properties of nilpotent algebras
Yuri Bahturin, Alexander Olshanskii
We study general nilpotent algebras. The results obtained are new even for the classical algebras, such as associative or Lie algebras. We single out certain generic properties of…
Steep uncountable groups
Samuel M. Corson, Alexander Olshanskii, Olga Varghese
We produce a simple group of cardinality which is Artinian (every strictly descending chain of subgroups is finite), satisfies a Burnside law and such that for each…
Nilpotent algebras, implicit function theorem, and polynomial quasigroups
Yuri Bahturin, Alexander Olshanskii
We study finite-dimensional nonassociative algebras. We prove the implicit function theorem for such algebras. This allows us to establish a correspondence between such algebras an…