On the theory of braid groups
    
    
  
  
  
      
      
      
        
Sbornik. Mathematics, Tome 76 (1993) no. 1, pp. 123-153
    
  
  
  
  
  
    
      
      
        
      
      
      
    Voir la notice de l'article provenant de la source Math-Net.Ru
            
              			It is proved that in the braid group $B_n$ for $n\geqslant3$ any proper verbal subgroup $V(B_n)$ defined by a finite set of words $V$ has infinite width relative to $V$. In addition, it is proved that in a colored braid group the taking of roots is unique and that the only element conjugate to its inverse is the identity.
			
            
            
            
          
        
      @article{SM_1993_76_1_a6,
     author = {V. G. Bardakov},
     title = {On the theory of braid groups},
     journal = {Sbornik. Mathematics},
     pages = {123--153},
     publisher = {mathdoc},
     volume = {76},
     number = {1},
     year = {1993},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1993_76_1_a6/}
}
                      
                      
                    V. G. Bardakov. On the theory of braid groups. Sbornik. Mathematics, Tome 76 (1993) no. 1, pp. 123-153. http://geodesic.mathdoc.fr/item/SM_1993_76_1_a6/