Statistical properties of groups with finite presentation

Let M(m) be a free group on m fixed generators, and k a fixed number. We study properties of the quotient group of L(m) by the normal subgroup generated by ''randomly'' chosen elements r(1)..., r(k) of L(m). 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. (C) 1995 Academic Press, Inc.