The Kervaire-Laudenbach conjecture and presentations of simple groups

Details The Kervaire-Laudenbach conjecture and presentations of simple groups The Kervaire-Laudenbach conjecture and presentations of simple groups

2004-09-09

arxiv.org/abs/math/0409146v1

Algebra and Logic Volume 44 (2005), Number 4, pp. 219 - 242. Translated from Algebra i Logika, Vol. 44 (2005), No. 4, pp. 399-

Mathematics

Group Theory

20 pages, 13 figures

Scientific paper

10.1007/s10469-005-0023-y

The statement ``no nonabelian simple group can be obtained from a nonsimple group by adding one generator and one relator" 1) is equivalent to the Kervaire--Laudenbach conjecture; 2) becomes true under the additional assumption that the initial nonsimple group is either finite or torsion-free. Key words: Kervaire--Laudenbach conjecture, relative presentations, simple groups, car motion, cocar comotion. AMS MSC: 20E32, 20F05, 20F06.

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