Maximum order of periodic outer automorphisms of a free group

Let F-n be a free group with rank n, and denote by Out F-n its outer automo tphism group. For arbitrary n, consider the orders of periodic elements in Out F-n or, equivalently, the orders of finite cyclic subgroups of Out F-n. By considering group actions on finite connected graphs, we obtained the n umber-theoretical characterization of these orders. Comparing the results w ith those for cyclic subgroups of finite symmetric groups asymptotic estima tion for the maximum order c(n) is derived. (C) 2000 Academic Press.