RESIDUAL PROPERTIES OF FREE PRODUCTS

Let L be a class of groups. We give sufficient conditions ensuring that a free product of residually L groups is again residually L, and analogous conditions are given for LE-L groups. As a corollary, we obtain that the class of residually amenable groups and the one of locally embeddable into amenable (LEA) groups are closed under taking free products. Moreover, we consider the pro-L topology and we characterize special HNN extensions and amalgamated free products that are residually L, where L is a suitable class of groups. In this way, we describe special HNN extensions and amalgamated free products that are residually amenable.