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math.GR2026
Solvability of unimodular equations in groups and Lie algebras
Anton A. Klyachko, Mikhail A. Mikheenko, Alexander Yu. Olshanskii
Our results imply, 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 t…
math.GR2026
On a generalization of Shmel'kin's theorem
Mikhail A. Mikheenko
It is known that every nilpotent group contains solution of every finite unimodular system of equatiuons over itself. This statement, however, is not true for infinite systems. Mor…