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Equations in free groups


In this project we wish to explore theoretical, as well as practical, aspects of solving equations in free groups. We will first consider a particular type of equation that occurs while solving the endomorphism problem in free groups. We say that the endom orphism problem is solvable for an element W in a group G if it can be decided effectively whether or not, given U in G, there is an endomorphism of G sending Wto U. We aim to display a polynomial-time algorithm that solves the endomorphism problem in free groups and also analyse the endomorphism problem from the perspective of generic-time complexity as developed by Schupp, Kapovich, Myasnikov and Shpilrain.

Another goal of this project is the classification of equations in free groups in the following sense. We call a group G separable with respect to a class of equations if, for every equation in the class with no solution in G, there is a finite quotient of G in which the equation has no solution. We want to determine what classes of equations the free groups are separable with respect to.

Call for proposal

See other projects for this call

Funding Scheme

EIF - Marie Curie actions-Intra-European Fellowships