9 citations · 29 across the 26 of their papers we have counts for
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Amalgamated Products of Groups II: Measures of Random Normal Forms
Elizaveta Frenkel, Alexei G. Myasnikov, Vladimir N. Remeslennikov
Let be an amalgamated product of finite rank free groups , and . We introduce atomic measures and corresponding asymptotic densities on a se…
A polynomial bound on solutions of quadratic equations in free groups
Igor Lysenok, Alexei Myasnikov
We provide polynomial upper bounds on the size of a shortest solution for quadratic equations in a free group. A similar bound is given for parametric solutions in the description…
Random equations in nilpotent groups
Robert Gilman, Alexei Myasnikov, Vitalii Romankov
In this paper we study satisfiability of random equations in an infinite finitely generated nilpotent group G. We show that the set SAT(G,k) of all equations in k > 1 variables ove…
The Finitary Andrews-Curtis Conjecture
Alexandre V. Borovik, Alexander Lubotzky, Alexei G. Myasnikov
The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis gr…