Commentarii Mathematici Helvetici

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Volume 72, Issue 1, 1997, pp. 16–29
DOI: 10.1007/PL00000364

Published online: 1997-03-31

Central quotients of biautomatic groups

John Loftin[1]

(1) Rutgers University, Newark, USA

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 ${\bf Z}^n$. Among other applications, a question of Gersten and Short is settled by showing that direct factors of biautomatic groups are biautomatic.

Keywords: Biautomatic groups, quasi-isometries, quasi-isometric sections, central extensions

Loftin John: Central quotients of biautomatic groups. Comment. Math. Helv. 72 (1997), 16-29. doi: 10.1007/PL00000364