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.
If G is a finitely presented group then its Dehn function—or its isoperimetric inequality—is of interest. For example, G satisfies a linear isoperi-metric inequality iff G is negatively curved (or hyperbolic in the sense of Gro-mov). Also, if G possesses an automatic structure then G satisfies a quadratic isoperimetric inequality. We investigate the effect… (More)
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)
ii To my mom, dad, sister, and grandparents. iii ACKOWLEDGMETS I am heartily thankful to Dr. Thomas F. Hain who introduced this research topic to me. He has been the source of motivation throughout this research. This research is due to his support and encouragement. He has been a great mentor to me for two and half years. I am thankful for his help and… (More)