(1974, J. London Math. Soc. 2, 160-164) showed that outer automorphism groups of fundamental groups of closed orientable surfaces are residually finite. Here we generalize her result by showing that outer automorphism groups of generalized free products of two free groups amalgamating a maximal cyclic subgroup are residually finite. From this it follows that mapping class groups of closed orientable and nonorientable surfaces are residually finite. The latter answers a question raised by A. M. Gaglione.  2001 Elsevier Science

Communicated by J. HowieIn [5] Grossman showed that outer automorphism groups of free groups and of fundamental groups of compact orientable surfaces are residually finite. In this paper we introduce the concept of "Property E" of groups and show that certain generalized free products and HNN extensions have this property. We deduce that the outer automorphism groups of finitely generated non-triangle Fuchsian groups are residually finite.

It is well known that Seifert 3-manifold groups are residually finite. Niblo [J. Pure Appl. Algebra 78 (1992) 77-84] showed that they are double coset separable. Applying this result we show that, except for some special cases, most of the Seifert 3-manifold groups are conjugacy separable.  2004 Elsevier Inc. All rights reserved.

In general polygonal products of finitely generated torsion-free nilpotent groups amalgamating cyclic subgroups need not be residually finite. In this paper we prove that polygonal products of finitely generated torsion-free nilpotent groups amalgamating maximal cyclic subgroups such that the amalgamated cycles generate an isolated subgroup in the vertex group containing them, are residually finite. We also prove that, for finitely generated torsion-free nilpotent groups, if the subgroups generated by the amalgamated cycles have the same nilpotency classes as their respective vertex groups, then their polygonal product is residually finite.

We derive a criterion for a generalized free product of groups to be cyclic subgroup separable. We see that most of the known results for cyclic subgroup separability are covered by this criterion, and we apply the criterion to polygonal products of groups. We show that a polygonal product of finitely generated abelian groups, amalgamating cyclic subgroups, is cyclic subgroup separable.