Groups, Geometry, and Dynamics
Full-Text PDF (316 KB) | Metadata | Table of Contents | GGD summary
Published online: 2009-09-30
Periodic quotients of hyperbolic and large groupsAshot Minasyan, Alexander Olshanskii and Dmitriy Sonkin (1) University of Southampton, United Kingdom
(2) Vanderbilt University, Nashville, United States
(3) University of Virginia, Charlottesville, United States
Let G be either a non-elementary (word)
hyperbolic group or a large group (both in the sense of Gromov). In this article we describe
several approaches for constructing continuous families of periodic
quotients of G with various properties.
The first three methods work for any non-elementary hyperbolic group, producing three different continua of periodic quotients of G. They are based on the results and techniques, that were developed by Ivanov and Olshanskii in order to show that there exists an integer n such that G/Gn is an infinite group of exponent n.
The fourth approach starts with a large group G and produces a continuum of pairwise non-isomorphic periodic residually finite quotients.
Speaking of a particular application, we use each of these methods to give a positive answer to a question of Wiegold from the Kourovka Notebook.
Keywords: Hyperbolic groups, large groups, periodic quotients
Minasyan Ashot, Olshanskii Alexander, Sonkin Dmitriy: Periodic quotients of hyperbolic and large groups. Groups Geom. Dyn. 3 (2009), 423-452. doi: 10.4171/GGD/65