Cosets of Sylow p-subgroups and a Question of Richard Taylor

2012/08/27 by Daniel Goldstein, Robert M. Guralnick, Goldstein, Daniel +1
Mathematics · #11R34 (Secondary) #20D06 (Primary) 11F80 #20D20 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.GR #math.NT #msc:11F80 #msc:11R34 #msc:20D06 #msc:20D20

paper · pdf · doi:10.48550/arxiv.1208.5283

arxiv created 2012/08/27 · openalex publication_date 2012/08/27 · arxiv updated 2012/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for any prime p there exist infinitely many finite simple groups G with a coset xP of a Sylow p-subgroup P of G such that every element of xP has order divisible by p. John Thompson proved this for p=2 in 1967 answering a question of Lowell Paige. This result is used to answer a question of Richard Taylor on adequate representations.

Citations

• On the automorphy of l-adic Galois representations with small residual image

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