Random (r,s)-generation of finite classical groups

Martin W. Liebeck; Aner Shalev

doi:10.1112/S0024609301008827

Random (r,s)-generation of finite classical groups

Martin W. Liebeck^*, Aner Shalev

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

A proof is given that for primes r, s, not both 2, and for finite simple classical groups G of sufficiently large rank, the probability that two randomly chosen elements in G of orders r and s generate G tends to 1 as |G| ∞.

Original language	English
Pages (from-to)	185-188
Number of pages	4
Journal	Bulletin of the London Mathematical Society
Volume	34
Issue number	2
DOIs	https://doi.org/10.1112/S0024609301008827
State	Published - Mar 2002

Bibliographical note

Funding Information:
The authors thank the Institute of Advanced Study at the Hebrew University for support. The second author acknowledges the support of a grant from the Israel Science Foundation.

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10.1112/S0024609301008827

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title = "Random (r,s)-generation of finite classical groups",

abstract = "A proof is given that for primes r, s, not both 2, and for finite simple classical groups G of sufficiently large rank, the probability that two randomly chosen elements in G of orders r and s generate G tends to 1 as |G| ∞.",

author = "Liebeck, \{Martin W.\} and Aner Shalev",

note = "Funding Information: The authors thank the Institute of Advanced Study at the Hebrew University for support. The second author acknowledges the support of a grant from the Israel Science Foundation.",

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AB - A proof is given that for primes r, s, not both 2, and for finite simple classical groups G of sufficiently large rank, the probability that two randomly chosen elements in G of orders r and s generate G tends to 1 as |G| ∞.

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Random (r,s)-generation of finite classical groups

Abstract

Bibliographical note

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