Complete rewriting system and growth series for extended generalized hecke groups

Abstract

In this paper, we obtain a complete rewriting system for monoid presentation of generalized extended Hecke group (H) over bar (p,q), which is firstly defined in [8]. It gives an algorithm for getting normal form of elements and hence solving the word problem in this group. By using the normal form structure of elements of (H) over bar (p,q), we also calculate growth series.