Periodic groups and their automorphisms

Sun, 25/01/2015 - 12:00
The free Burnside group of exponent n, B(r,n), is the quotient of the free group of rank r by the subgroup generated by all n-th powers. This group was introduced in 1902 by W. Burnside who asked whether it is finite or not. This problem motivated many developments in group theory. In 1968 P.S. Novikov and S.I. Adian made a breakthrough by proving that if n is sufficiently large then B(r,n) is infinite. In this talk we will focus on the symmetries of B(r,n). More precisely we will consider on the outer automomorphism group of B(r,n). Among other things, we will see that it inherits some properties coming from the outer automorphism group of free groups.