Central quotients of biautomatic groups

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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 Sn-1, associated to a biautomatic structure on Zn. Among other applications, a question of Gersten and Short is settled by showing that direct factors of biautomatic groups are biautomatic.

Original languageEnglish (US)
Pages (from-to)16-29
Number of pages14
JournalCommentarii Mathematici Helvetici
Volume72
Issue number1
DOIs
StatePublished - 1997

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Biautomatic groups
  • Central extensions
  • Quasi-isometric sections
  • Quasi-isometries

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