REWRITING-SYSTEMS FOR COXETER GROUPS

[摘要] A finite complete rewriting system for a group is a finite presentation which gives a solution to the word problem and a regular language of normal forms for the group. In this paper it is shown that the fundamental group of an orientable closed surface of genus g has a finite complete rewriting system, using the usual generators a1, ..., a(g), b1, ..., b(g) along with generators representing their inverses. Constructions of finite complete rewriting systems are also given for any Coxeter group G satisfying one of the following hypotheses. (1) G has three or fewer generators. (2) G does not contain a special subgroup of the form [s(i), s(j), s(k)\s(i)2 = s(j)2 = s(k)2 = (s(i)s(j))2 = (s(i)S(k))m = (s(j)s(k))n = 1] with m and n both finite and not both equal to two.

[发布日期] 1994-03-07