Babai’s conjecture for high-rank classical groups with random generators

Sean Eberhard; Urban Jezernik

doi:10.1007/s00222-021-01065-x

Babai’s conjecture for high-rank classical groups with random generators

Sean Eberhard
, Urban Jezernik^*

^*Corresponding author for this work

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

9 Citations (Scopus)

200 Downloads (Pure)

Abstract

Let G= SCl _n(q) be a quasisimple classical group with n large, and let x₁, … , x_k∈ G be random, where k≥ q^C. We show that the diameter of the resulting Cayley graph is bounded by q²n^O⁽¹⁾ with probability 1 - o(1). In the particular case G= SL _n(p) with p a prime of bounded size, we show that the same holds for k= 3.

Original language	English
Pages (from-to)	149-210
Number of pages	62
Journal	Inventiones Mathematicae
Volume	227
Issue number	1
Early online date	17 Aug 2021
DOIs	https://doi.org/10.1007/s00222-021-01065-x
Publication status	Published - Jan 2022
Externally published	Yes

Bibliographical note

Funding Information:
S. Eberhard has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 803711) U. Jezernik has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 741420).

Publisher Copyright:
© 2021, The Author(s).

ASJC Scopus subject areas

General Mathematics

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10.1007/s00222-021-01065-xLicence: CC BY

Babai’s conjecture for high-rank classical groups with random generators
Copyright 2021 the authors. This is an open access article published under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.
Final published version, 650 KBLicence: CC BY

Cite this

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author = "Sean Eberhard and Urban Jezernik",

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N2 - Let G= SCl n(q) be a quasisimple classical group with n large, and let x1, … , xk∈ G be random, where k≥ qC. We show that the diameter of the resulting Cayley graph is bounded by q2nO(1) with probability 1 - o(1). In the particular case G= SL n(p) with p a prime of bounded size, we show that the same holds for k= 3.

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Babai’s conjecture for high-rank classical groups with random generators

Abstract

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