Outer Automorphism Groups of Polygonal Products of Certain Conjugacy Separable Groups

Abstract

Abstract. Grossman [7] showed that certain cyclically pinched 1-relator groups have residually finite outer automorphism groups. In this paper we prove that tree products of finitely generated free groups amalgamating maximal cyclic subgroups have residually finite outer automorphism groups. We also prove that polygonal products of finitely generated central subgroup separable groups amalgamating trivial intersecting central subgroups have residually finite outer automorphism groups.

Conjugacy separability and outer automorphism groups of certain HNN extensions

“…Recently, Allenby, Kim, Tang, Chai and Choi in several papers [1,2,7,13,16], have made important contributions to the study of the residual finiteness of outer automorphism groups of various groups. In [1], Allenby, Kim and Tang improved on Grossman's results by proving that the outer automorphism groups of generalized free products of two free groups amalgamating a maximal cyclic subgroup are residually finite.…”

“…More recently Kim in [13], proved that the outer automorphism groups of the polygonal products of four polycyclic-by-finite groups amalgamating central subgroups with trivial intersection are residually finite. Very recently Kim and Tang [16] proved that the outer automorphism groups of tree products of finitely generated free groups amalgamating maximal cyclic subgroups and the outer automorphism groups of polygonal products of finitely generated central subgroup separable groups amalgamating central subgroups with trivial intersection are residually finite. As a consequence outer automorphism groups of polygonal products of finitely generated abelian groups amalgamating trivial intersecting subgroups are residually finite.…”