We study the property of tame combability for groups. We show that quasi-isometries preserve this property. We prove that an amalgamation, A * C B, where C is finitely generated, is tame combable iff both A and B are. An analogous result is obtained for HNN extensions. And we show that all one-relator groups are tame combable.
We study the Dehn functions of amalgamations, introducing the notion of strongly undistorted subgroups. Using this, we give conditions under which taking an amalgamation does not increase the Dehn function, generalizing one aspect of the combination theorem of Bestvina and Feighn. To obtain examples of strongly undistorted subgroups, we define and study the… (More)