On the generators of the kernels of hyperbolic group presentations

• Published in: Algebra and Discrete Mathematics
• Date: 2011
• ISSN: 1726-3255
• Main Author: Chaynikov, V.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2011
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/154774
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On the generators of the kernels of hyperbolic group presentations / V. Chaynikov// Algebra and Discrete Mathematics. — 2011. — Vol. 11, № 2. — С. 18–50. — Бібліогр.: 11 назв. — англ.

In this paper we prove that if R is a (not necessarily finite) set of words satisfying certain small cancellation condition in a hyperbolic group G then the normal closure of R is free. This result was first presented (for finite set R) by T. Delzant [Delz] but the proof seems to require some addit...