污污草莓视频

Title: Combination of groups with hyperbolically embedded subgroups and groups with well-defined relative dehn functions.

Abstract: Hyperbolically embedded subgroups were defined by F. Dahmani, V. Guirardel and D. Osin as a generalization of peripheral structure of relatively hyperbolic groups. We revisit the definition of these subgroups using the Bowditch graph approach which was described by E. Martinez Pedroza and F. Rashid. Then we prove a combination theorem for hyperbolically embedded subgroups where each edge group of the splitting graph of groups is conjugate into a "subgroup" of a peripheral structure of the adjacent vertex group. Moreover, after defining groups with well-defined relative dehn function, we provide a similar combination theorem for these groups which follows from constructing a Cayley_Abel graph in the first part of this talk. The method of proof provides lower and upper bounds of the relative Dehn functions in terms of the relative Dehn functions of the vertex groups. This is a joint work with E. Martinez Pedroza.