2 citations · 3 across the 4 of their papers we have counts for
7 papers
A sample iterated small cancellation theory for groups of Burnside type
Igor Lysenok
We develop yet another technique to present the free Burnside group of odd exponent with generators as a group satisfying a certain iterated small cancellation…
Orientable quadratic equations in free metabelian groups
Igor Lysenok, Alexander Ushakov
We prove that the Diophantine problem for orientable quadratic equations in free metabelian groups is decidable and furthermore, NP-complete. In the case when the number of variabl…
Commutator width in the first Grigorchuk group
Laurent Bartholdi, Thorsten Groth, Igor Lysenok
Let be the first Grigorchuk group. We show that the commutator width of is : every element is a product of two commutators, and also of six conjugates of $a…
Quadratic equations in the Grigorchuk group
Igor Lysenok, Alexei Miasnikov, Alexander Ushakov
We provide an algorithm which, for a given quadratic equation in the Grigorchuk group determines if it has a solution. As a corollary to our approach, we prove that the group has a…
Spherical quadratic equations in free metabelian groups
Igor Lysenok, Alexander Ushakov
We prove that the Diophantine problem for spherical quadratic equations in free metabelian groups is solvable and, moreover, NP-complete
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…