7 citations · 13 across the 7 of their papers we have counts for
7 papers
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…
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…
Unimodular equations which do not preserve the derived length of a group
Mikhail A. Mikheenko
It is a known fact that any unimodular equation over an abelian group has a solution in that group itself. It is also known that for metabelian groups this does not hold; moreover,…
Infinite systems of equations in abelian and nilpotent groups
Mikhail A. Mikheenko
Every abelian (and even every nilpotent) group contains a solution of any finite unimodular system of equations over itself. However, this is not true for infinite systems. We dedu…
On -nonsingular systems of equations over solvable groups
Mikhail A. Mikheenko
Any group that has a subnormal series, in which all factors are abelian and all except the last one are -torsion-free, can be embedded into a group with a subnormal series of t…
Equations over solvable groups
Anton A. Klyachko, Mikhail A. Mikheenko, Vitaly A. Roman'kov
Not any nonsingular equation over a metabelian group has solution in a larger metabelian group. However, any nonsingular equation over a solvable group with a subnormal series with…
Yet another Freiheitssatz: Mating finite groups with locally indicable ones
Anton A. Klyachko, Mikhail A. Mikheenko
The main result includes as special cases on the one hand, the Gerstenhaber--Rothaus theorem (1962) and its generalisation due to Nitsche and Thom (2022) and, on the other hand, th…