Karpuz, Eylem GuzelAtes, FiratCevik, A. Sinan2020-03-262020-03-2620150035-75961945-3795https://dx.doi.org/10.1216/RMJ-2015-45-4-1165https://hdl.handle.net/20.500.12395/32197In this paper, we obtain Crobner-Shirshov (non-commutative) bases for the n-extended affine Weyl group (W) over tilde of type A(1), elliptic Weyl groups of types A(1)((1,1)) A(1)((1,1))* and the 2-extended affine Weyl group of type A(2)((1,1)) with a generator system of a 2-toroidal sense. It gives a new algorithm for getting normal forms of elements of these groups and hence a new algorithm for solving the word problem in these groups.en10.1216/RMJ-2015-45-4-1165info:eu-repo/semantics/closedAccessGrobner-Shirshov basispresentationWeyl groupArticle45411651175Q2WOS:000365160600008Q4