The free group on n generators modulo n + u random relations as n goes to infinity

Yuan Liu, Melanie Matchett Wood

Research output: Contribution to journalArticlepeer-review

Abstract

We show that, as n goes to infinity, the free group on n generators, modulo n + u {n+u} random relations, converges to a random group that we give explicitly. This random group is a non-abelian version of the random abelian groups that feature in the Cohen-Lenstra heuristics. For each n, these random groups belong to the few relator model in the Gromov model of random groups.

Original languageEnglish (US)
Pages (from-to)123-166
Number of pages44
JournalJournal fur die Reine und Angewandte Mathematik
Volume2020
Issue number762
DOIs
StatePublished - May 1 2020
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'The free group on n generators modulo n + u random relations as n goes to infinity'. Together they form a unique fingerprint.

Cite this