Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


The product replacement algorithm and Kazhdan’s property (T)
HTML articles powered by AMS MathViewer

by Alexander Lubotzky and Igor Pak
J. Amer. Math. Soc. 14 (2001), 347-363
Published electronically: October 18, 2000


The “product replacement algorithm” is a commonly used heuristic to generate random group elements in a finite group $G$, by running a random walk on generating $k$-tuples of $G$. While experiments showed outstanding performance, the theoretical explanation remained mysterious. In this paper we propose a new approach to the study of the algorithm, by using Kazhdan’s property (T) from representation theory of Lie groups.
Similar Articles
Bibliographic Information
  • Alexander Lubotzky
  • Affiliation: Department of Mathematics, Hebrew University, Givat Ram, Jerusalem 91904, Israel
  • MR Author ID: 116480
  • Email:
  • Igor Pak
  • Affiliation: Department of Mathematics, Yale University, New Haven, Connecticut 06520
  • Address at time of publication: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • MR Author ID: 293184
  • ORCID: 0000-0001-8579-7239
  • Received by editor(s): January 5, 2000
  • Received by editor(s) in revised form: August 23, 2000
  • Published electronically: October 18, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 14 (2001), 347-363
  • MSC (2000): Primary 60B15; Secondary 05C25, 22D10, 60J10
  • DOI:
  • MathSciNet review: 1815215