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The statement ``no nonabelian simple group can be obtained from a nonsimplegroup 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 nonsimplegroup is either finite or torsion-free.  Key words: Kervaire--Laudenbach conjecture, relative presentations, simplegroups, car motion, cocar comotion.  AMS MSC: 20E32, 20F05, 20F06.Comment: 20 pages, 13 figure

The Kervaire-Laudenbach Conjecture and Presentations of Simple Groups