Details:
Title  Relative Gr\"obnerShirshov bases for algebras and groups.  Author(s)  Leonid A. Bokut, K.P. Shum  Type  Article in Journal  Abstract  The notion of a relative GröbnerShirshov basis for algebras and groups is introduced. The relative composition lemma and relative (composition)diamond lemma are established. In particular, it is shown that the relative normal forms of certain groups arising from Malcev's embedding problem are the irreducible normal forms of these groups with respect to their relative GröbnerShirshov bases. Other examples of such groups are given by showing that any group $ G$ in a Tits system $ (G, B, N,S)$ has a relative ($ B$)GröbnerShirshov basis such that the irreducible words are the Bruhat words of $ G$.  ISSN  10610022; 15477371/e 
URL 
http://www.ams.org/journals/spmj/20081906/S106100220801025X/home.html 
Language  English  Journal  St. Petersbg. Math. J.  Volume  19  Number  6  Pages  867881  Publisher  American Mathematical Society (AMS), Providence, RI  Year  2008  Edition  0  Translation 
No  Refereed 
No 
