23 citations · 112 across the 42 of their papers we have counts for
6 papers · 2 filters
Definable sets in a hyperbolic group
Olga Kharlampovich, Alexei Myasnikov
We give a description of definable sets in a free non-abelian group and in a torsion-free non-elementary hyperbolic group that follows from our work on t…
From automatic structures to automatic groups
Olga Kharlampovich, Bakhadyr Khoussainov, Alexei Miasnikov
In this paper we introduce the concept of a Cayley graph automatic group (CGA group or graph automatic group, for short) which generalizes the standard notion of an automatic group…
Linear estimates for solutions of quadratic equations in free groups
Olga Kharlampovich, Alina Vdovina
We prove that in a free group the length of the value of each variable in a minimal solution of a standard quadratic equation is bounded by for orientable equation and by $12s…
Infinite words and universal free actions
Olga Kharlampovich, Alexei Myasnikov, Denis Serbin
This is the second paper in a series of three, where we take on the unified theory of non-Archimedean group actions, length functions and infinite words. Here, for an arbitrary gro…
Approximation of Geodesics in Metabelian Groups
O. Kharlampovich, A. Mohajeri Moghaddam
It is known that the bounded Geodesic Length Problem in free metabelian groups is NP-complete (in particular, the Geodesic Problem is NP-hard). We construct a 2-approximation polyn…
-free groups are CAT(0)
Inna Bumagin, Olga Kharlampovich
We show that every group with free -length function is CAT(0).