Abstract
In this article, 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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Notes
Communicated by A. Thrull.