The Kervaire-Laudenbach conjecture and presentations of simple groups
  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. 
Anton A. Klyachko