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The largest character degree and the Sylow subgroups of finite groups

Guohua Qian

Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu 215500, P. R. China

E-mail Address: ghqian@cslg.cn

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and

Yong Yang

Key Laboratory of Group & Graph Theories and Applications, Chongqing University of Arts and Sciences, Chongqing, China

Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX 78666, USA

E-mail Address: yang@txstate.edu

Corresponding author.

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https://doi.org/10.1142/S0219498816500663Cited by:3 (Source: Crossref)

Abstract

Let $P$ $P$ be a Sylow $p$ $p$ -subgroup and $b (G)$ $b (G)$ be the largest irreducible character degree of a finite nonabelian group $G$ $G$ . Then $∣ ∣ P / O_{p} (G) ∣ ∣ \leq {(b {(G)}^{p} / p)}^{\frac{1}{p - 1}}$ $| P / O_{p} (G) | \leq {(b {(G)}^{p} / p)}^{\frac{1}{p - 1}}$ .

Communicated by I. M. Isaacs

Keywords:

AMSC: 20C15

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