Free products of groups have no outer normal automorphisms

An automorphism of an arbitrary group is called normal if all subgroups of this group are left invariant by it. Lubotski 1] and Lue 2] showed that every normal automorphism of a noncyclic free group is inner. Here we prove that every normal automorphism of a nontrivial free product of groups is inner as well. Supported by RFFR grant No. 13-011-1513. Translated fromAlgebra i Logika, Vol. 35, No. 5, pp. 562–566, September–October, 1996.