TY - JOUR
T1 - The free group on n generators modulo n + u random relations as n goes to infinity
AU - Liu, Yuan
AU - Wood, Melanie Matchett
N1 - Publisher Copyright:
© 2020 Walter de Gruyter GmbH, Berlin/Boston 2020 National Science Foundation DMS-1652116 DMS-1301690 This work was done with the support of an American Institute of Mathematics Five-Year Fellowship, a Packard Fellowship for Science and Engineering, a Sloan Research Fellowship, a Vilas Early Career Investigator Award, and National Science Foundation grants DMS-1652116 and DMS-1301690.
PY - 2020/5/1
Y1 - 2020/5/1
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/85056192863
UR - https://www.scopus.com/pages/publications/85056192863#tab=citedBy
U2 - 10.1515/crelle-2018-0025
DO - 10.1515/crelle-2018-0025
M3 - Article
AN - SCOPUS:85056192863
SN - 0075-4102
VL - 2020
SP - 123
EP - 166
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 762
ER -