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math.GR2011
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…
math.GR2008
Cayley Graph Expanders and Groups of Finite Width
Norbert Peyerimhoff, Alina Vdovina
We present new infinite families of expander graphs of vertex degree 4, which is the minimal possible degree for Cayley graph expanders. Our first family defines a tower of coverin…