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

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

2010-09-28

arxiv.org/abs/1009.5434v2

Mathematics

Group Theory

Updated the introduction based on referee's report

Scientific paper

In this paper, we show that if $p$ is a prime and $G$ is a $p$-solvable
group, then $| G:O_p (G) |_p \le (b(G)^p/p)^{1/(p-1)}$ 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 $| G:O_p (G) |_p \le b(G)$.

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