Statistical Properties of Groups with Finite Presentation

AbstractLet Mm be a free group on m fixed generators, and k a fixed number. We study properties of the quotient group of Lm by the normal subgroup generated by "randomly" chosen elements r1..., rk of Lm. We prove that, in some statistical sense, these groups have "generic" properties for k = 2: they are "generically" hyperbolic (in M. Gromov′s sense), of cohomological dimension 2 and their boundary is a Menger′s curve. Moreover, it is easy to give explicit examples of such groups