Hall's Theorem for limit groups
arXiv:math/0605546
Abstract
A celebrated theorem of Marshall Hall Jr. implies that finitely generated free groups are subgroup separable and that all of their finitely generated subgroups are retracts of finite-index subgroups. We use topological techniques inspired by the work of Stallings to prove that all limit groups share these two properties. This answers a question of Sela.
39 pages, 4 figures, added a double-coset-separability result, to appear in GAFA