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

DOI10.1007/s00222-021-01065-xOpenAlexW3194226021WikidataQ123348305 ScholiaQ123348305MaRDI QIDQ2073762

Sean Eberhard, Urban Jezernik

Publication date: 8 February 2022

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.09990

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Special aspects of infinite or finite groups (20Fxx) Abstract finite groups (20Dxx)

Cites Work

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• Fibers of word maps and some applications.
• Random generators of the symmetric group: diameter, mixing time and spectral gap.
• Expansion in finite simple groups of Lie type.
• The Waring problem for finite simple groups.
• Approximate subgroups of linear groups.
• Characters of symmetric groups: sharp bounds and applications.
• Discrete groups, expanding graphs and invariant measures. With an appendix by Jonathan D. Rogawski
• Isometrien von Vektorräumen. I
• On the diameter of permutation groups
• On the minimal degrees of projective representations of the finite Chevalley groups
• Generalizations of the Kolmogorov-Barzdin embedding estimates
• Diameter of Cayley graphs of \(\mathrm{SL}(n,p)\) with generating sets containing a transvection
• Growth and generation in \(\text{SL}_2(\mathbb{Z}/p\mathbb{Z})\).
• On the diameter of permutation groups.
• Applications of character estimates to statistical problems for symmetric group
• The probability of generating a finite classical group
• On the shortest identity in finite simple groups of Lie type
• Symmetric Random Walks on Groups
• A new proof of Friedman's second eigenvalue theorem and its extension to random lifts
• Growth in finite simple groups of Lie type
• A proof of Alon’s second eigenvalue conjecture and related problems
• Random Cayley graphs and expanders
• The action of a few permutations onr-tuples is quickly transitive
• Girth, words and diameter
• Random generation of the special linear group
• CHARACTER LEVELS AND CHARACTER BOUNDS
• An improved diameter bound for finite simple groups of Lie type
• A diameter bound for finite simple groups of large rank
• On the conjugacy classes in the unitary, symplectic and orthogonal groups
• The probability of generating the symmetric group
• Diameters of finite simple groups: sharp bounds and applications

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