Maximum order of finite Abelian subgroups in the outer automorphism group of a rank n free group

Let F-n be a free group of rank n. Denote by Out F-n its outer automorphism group, that is, its automorphism group modulo its inner automorphism group . For arbitrary n, by considering group actions on finite connected graphs, we derived the maximum order of finite abelian subgroups in Out F-n. Moreo ver, it is shown that the subgroups reaching this maximum order can be dete rmined up to isomorphisms. (C) 2001 Academic Press.