Finite simple groups of Lie type as expanders.

DOI10.4171/JEMS/282zbMath1257.20016arXiv0904.3411OpenAlexW2060458304WikidataQ115212477 ScholiaQ115212477MaRDI QIDQ638776

Alexander Lubotzky

Publication date: 14 September 2011

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.3411

zbMATH Keywords

generatorsCayley graphsfinite simple groups of Lie typeprojective special linear groupsnon-Abelian finite simple groupsuniform expanders

Mathematics Subject Classification ID

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)

Related Items

On the product decomposition conjecture for finite simple groups, Covering and growth for group subsets and representations, Expander graphs and their applications, Groups of Lie type as products of \(\text{SL}_2\) subgroups., Model theory of finite and pseudofinite groups, How to pick a random integer matrix? (and other questions), Expander graphs in pure and applied mathematics, Non-expander Cayley Graphs of Simple Groups

Cites Work

• Explicit constructions of Ramanujan complexes of type \(\widetilde A_d\).
• Ramanujan complexes of type \(\widetilde A_d\)
• Small-diameter Cayley graphs for finite simple groups
• Proof of Peterson's conjecture for GL(2) over a global field of \(characteristic\quad p\).
• Ultraproducts and Chevalley groups
• A family of \(\widetilde A_n\)-groups
• Discrete groups, expanding graphs and invariant measures. Appendix by Jonathan D. Rogawski
• Existence and explicit constructions of \(q+1\) regular Ramanujan graphs for every prime power \(q\)
• Drinfeld shtukas and Langlands correspondence.
• Groups of Lie type as products of \(\text{SL}_2\) subgroups.
• Universal lattices and unbounded rank expanders.
• Symmetric groups and expander graphs.
• Uniform Kazhdan constant for some families of linear groups.
• New results on expanders
• Universal lattices and property \(\tau\)
• KAZHDAN CONSTANTS OF GROUP EXTENSIONS
• A product decomposition for the classical quasisimple groups
• Field Arithmetic
• Finite simple groups as expanders
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item