Book review of: T. Tao, Expansion in finite simple groups of Lie type

DOI10.1365/s13291-015-0130-1zbMath1348.00032OpenAlexW2344092485WikidataQ115238636 ScholiaQ115238636MaRDI QIDQ335012

Alain Valette

Publication date: 2 November 2016

Published in: Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1365/s13291-015-0130-1

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Generators, relations, and presentations of groups (20F05) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Simple groups: alternating groups and groups of Lie type (20D06) Probabilistic methods in group theory (20P05) External book reviews (00A17) Research exposition (monographs, survey articles) pertaining to group theory (20-02) Random walks on graphs (05C81) Arithmetic combinatorics; higher degree uniformity (11B30)

Cites Work

• Unnamed Item
• Expansion in finite simple groups of Lie type.
• Suzuki groups as expanders.
• Approximate subgroups of linear groups.
• Affine linear sieve, expanders, and sum-product
• Small-diameter Cayley graphs for finite simple groups
• Discrete groups, expanding graphs and invariant measures. With an appendix by Jonathan D. Rogawski
• Growth and generation in \(\text{SL}_2(\mathbb{Z}/p\mathbb{Z})\).
• Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\).
• Finite subgroups of algebraic groups
• Growth in finite simple groups of Lie type
• Expander graphs and their applications
• Finite simple groups as expanders