Title: On the exponent of congruence quotients of multi-EGS groups

Abstract: In 1902 Burnside asked whether a finitely generated torsion group has to be finite. The answer to this question is negative, and since the 1960s many examples of infinite finitely generated torsion groups have been found. Among these examples, some of the easiest turned out to be groups acting on trees: the Gupta-Sidki group, for instance, is an infinite finitely generated torsion group acting on a tree, it was first defined in 1983 and it finds its natural generalisation in the family of the so-called multi-EGS groups.

The fact that multi-EGS groups are infinite suggests that they are large in some sense. Another point that supports their "largeness" is the fact that they have infinite exponent. Moreover, given a multi-EGS group G, there is a canonical sequence {G_n} of finite quotients of G, known as the congruence quotients of G, such that the limit of the sequence of exponents exp(G_n) (as n tends to infinity) is equal to the exponent of G. Understanding how fast this sequence goes to infinity gives another piece of information to work out how large G is.

In this talk, after defining what a multi-EGS group is, we will solve this problem, providing an explicit formula for exp(G_n) and giving a sketch of the proof.