Codimension-1 subgroups and splittings of groups

[摘要] We show that under certain circumstances, a codimension-1 subgroup H of a finitely generated group G either provides a splitting of G as an amalgam or provides a codimension-1 subgroup of H. In particular, if G is hyperbolic and H is quasiconvex, one gets a descending sequence of codimension-1 subgroups, terminating at a splitting. In the process, we settle a conjecture of Kropholler and Roller for the case of quasiconvex subgroups of hyperbolic groups. (C) 1997 Academic Press.

[发布日期] 1997-03-15