@article {IOPORT.06059227, author = {Rodr{\'\i}guez, Jos\'e Gregorio and Toro, Margarita}, title = {Virtual knot groups and combinatorial knots.}, year = {2009}, journal = {S\~ao Paulo Journal of Mathematical Sciences}, volume = {3}, number = {2}, issn = {1982-6907}, pages = {299-316}, publisher = {Instituto de Matem\'atica e Estadistica da Universidade de S\~ao Paulo, S\~ao Paulo}, abstract = {Summary: {\it L.H. Kauffman} [Eur. J. Comb. 20, No. 7, 663--690 (1999; Zbl 0938.57006)] and {\it S.G. Kim}, [J. Knot Theory Ramifications 9, No. 6, 797--812 (2000; Zbl 0997.57017)] defined the group of a virtual knot by extending, in a natural way, the Wirtinger presentation of the fundamental group of classical knot. In this paper we present the group of a virtual knot by using the concept of combinatorial knot, introduced by {\it M.M. Toro Villegas} [Rev. Acad. Colomb. Cienc. Exactas, Fis. Nat. 28, No. 106, 79--86 (2004; Zbl 1102.57006)]. We show the advantages of this approach, that provides natural algorithms. We present examples of combinatorial knots whose groups have properties that are false, or unknown, in the category of the classical knots.}, identifier = {06059227}, }