Mathematics > Group Theory
arXiv:2606.24688 (math)
[Submitted on 23 Jun 2026]
Abstract:Fix an integer $m$ bigger than 2. We prove that if there exists a finite group with $mp+1$ Suylow $p$-subgroups, where $p$ is large enough, then $mp+1$ is prime. This improves on a theorem of M. Hall and is a partial answer to Brauer's Problem 26. Our proof uses techniques from analytic number theory, and it also raises new questions in that area.
Submission history
From: Jorge Urroz [view email]
[v1]
Tue, 23 Jun 2026 15:17:33 UTC (9 KB)
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