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 . Among other applications, a question of Gersten and Short is settled by showing that direct factors of biautomatic groups are biautomatic.
Cite this article
John Loftin, Central quotients of biautomatic groups. Comment. Math. Helv. 72 (1997), no. 1, pp. 16–29DOI 10.1007/PL00000364