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The Kervaire-Laudenbach Conjecture and Presentations of Simple Groups

2005; Springer Nature; Volume: 44; Issue: 4 Linguagem: Inglês

10.1007/s10469-005-0023-y

1573-8302

Anton A. Klyachko,

Homotopy and Cohomology in Algebraic Topology

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.