On the spread of finite simple groups

Robert M. Guralnick*, Aner Shalev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


The spread of a finite group is the maximal integer k so that for each k non-identity elements of G there is an element generating G with each of them. We prove an asymptotic result characterizing the finite simple groups of bounded spread. We also obtain estimates for the spread of the various families of finite simple groups, and show that it is at least 2, with possibly finitely many exceptions. The proofs involve probabilistic methods.

Original languageAmerican English
Pages (from-to)73-87
Number of pages15
Issue number1
StatePublished - 2003

Bibliographical note

Funding Information:
Th e first auth or acknowledges th e support of th e NSF; th e second auth or acknowledges th e support of th e Israel Science Foundation and th e h ospitality of USC; both auth ors acknowledge th e support and h ospitality of MSRI


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