Uniform expansion bounds for Cayley graphs of SL 2 (𝔽 p )

2008/03/01 by Jean Bourgain, Alex Gamburd · 32 citations
Mathematics · #Finite Group Theory Research #Advanced Algebra and Geometry #Analytic Number Theory Research

paper · pdf · doi:10.4007/annals.2008.167.625

Abstract

We prove that Cayley graphs of SL 2 (F p ) are expanders with respect to the projection of any fixed elements in SL(2, Z) generating a non-elementary subgroup, and with respect to generators chosen at random in SL 2 (F p ).

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Related

• Strong uniform expansion in SL(2,p)
• Expansion, Random Walks and Sieving in SL₂ (\mathbbF_p [t])
• Symmetric Groups and Expander Graphs
• Symmetric Groups and Expanders
• Random Cayley graphs and expanders