Central quotients of biautomatic groups

Abstract

The quotient of a biautomatic group by a subgroup of the center is shown to be biautomatic. The main tool used is the Neumann-Shapiro triangulation of S n-1, associated to a biautomatic structure on ${\mathbf{Z}}^n$. Among other applications, a question of Gersten and Short is settled by showing that direct factors of biautomatic groups are biautomatic.