We prove that a random group, in Gromov's density model with d < 1/16, satisfies a universal sentence sigma (in the language of groups) if and only if sigma is true in a non-abelian free group.

Publication:

Journal für die reine und angewandte Mathematik (Crelles Journal) 2024-08-15

http://dx.doi.org/10.1515/crelle-2024-0055

Author:

Olga Kharlampovich

Department of Mathematics and Statistics, CUNY Hunter College and Graduate Center, 695 Park Avenue, 10065, New York, USA

Rizos Sklinos

Institute of Mathematics, Academy of Mathematics and Systems Science, 55 Zhongguanchun, 100190, Beijing, P. R. China

Email: rizos.sklinos@amss.ac.cn