Bulletin of the
Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2015; 52(2): 363-366

Printed March 31, 2015

https://doi.org/10.4134/BKMS.2015.52.2.363

Copyright © The Korean Mathematical Society.

Two applications of Lewis' theorem on character degree graphs of solvable groups

Liguo He, Yuanhe Zhao, and Jianxing Bi

Shenyang University of Technology, Shenyang University of Technology, Liaoning University

Abstract

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In this note, we prove Gluck's conjecture and Isaacs-Navarro-Wolf Conjecture are true for the solvable groups with disconnected graphs by using Lewis' group structure theorem with respect to the disconnected character degree graphs.

Keywords: solvable group, character, fitting subgroup, non-vanishing element

MSC numbers: Primary 20C15

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