Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2019; 56(2): 501-504

Online first article September 7, 2018      Printed March 1, 2019

https://doi.org/10.4134/BKMS.b180353

Copyright © The Korean Mathematical Society.

Conjectures that solvable groups whose character graphs having diameter 3 satisfy

Qingyun Meng

Henan University of Technology

Abstract

In this note, we prove that Gluck's conjecture, Isaacs-Navarro -Wolf Conjecture and Taketa's inequality are true for solvable groups whose character graphs having diameter 3.

Keywords: finite solvable groups, character graphs, diameter 3, conjectures

MSC numbers: 20C15

Supported by: This work was supported by China Scholarship Council(CSC)and National Science Foundation Council (NSFC)(Grant Nos. 11601121, 11771356) and Science Foundation of Henan University of Technology (Grant No. 31490036)

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