Residual properties of the modular group and other free products

Martin W. Liebeck, Aner Shalev*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Using a probabilistic approach we establish new residual properties of the modular group PSL2 (ℤ), and of more general free products. We prove that the modular group is residually in any infinite collection of finite simple groups not containing a Suzuki group Sz(q) or a 4-dimensional symplectic group PSp4(q) with q a power of 2 or 3. This result is best possible, since the groups excluded are not quotients of the modular group. We also show that if S is a collection of classical groups of unbounded rank, then an arbitrary free product A * B of nontrivial finite groups, not both 2-groups, is residually S, and prove results about free products A * ℤ.

Original languageAmerican English
Pages (from-to)264-285
Number of pages22
JournalJournal of Algebra
Issue number1
StatePublished - 1 Oct 2003

Bibliographical note

Funding Information:
Research partially supported by a grant from the Israel Science Foundation for A.S. Corresponding author. E-mail address: (A. Shalev).


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