Bounding an index by the largest character degree of a solvable group

2010/09/28 by Mark L. Lewis, Lewis, Mark L.
Mathematics · #20C15 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Graph theory and applications #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1009.5434

openalex publication_date 2010/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that if p is a prime and G is a p-solvable group, then | G:O_p (G) |_p ≤ (b(G)^p/p)^1/(p-1) where b(G) is the largest character degree of G. If p is an odd prime that is not a Mersenne prime or if the nilpotence class of a Sylow p-subgroup of G is at most p, then | G:O_p (G) |_p ≤ b(G).

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