This article is cited in 8 papers

The Kervaire – Laudenbach Conjecture and Presentations of Simple Groups

A. A. Klyachko

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The statement “no non-Abelian simple group can be obtained from a non-simple one by adding one generator and one relator” first is equivalent to the Kervaire – Laudenbach conjecture, and second, becomes true under the additional assumption that an initial non-simple group is either finite or torsion free.

Keywords: Kervaire – Laudenbach conjecture, relative presentation, simple group, car motion, cocar comotion.

UDC: 512.543.7

Received: 18.11.2004

 English version: Algebra and Logic, 2005, 44:4, 219–242

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