Two applications of Lewis' theorem on character degree graphs of solvable groups
Bull. Korean Math. Soc. 2015 Vol. 52, No. 2, 363-366
https://doi.org/10.4134/BKMS.2015.52.2.363
Published online March 31, 2015
Liguo He, Yuanhe Zhao, and Jianxing Bi
Shenyang University of Technology, Shenyang University of Technology, Liaoning University
Abstract : 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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