Real strongly monolithic characters of finite groups

Erkoç T., Demir Ö.

RICERCHE DI MATEMATICA, vol.74, no.5, pp.2653-2659, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 74 Issue: 5
  • Publication Date: 2025
  • Doi Number: 10.1007/s11587-025-00984-8
  • Journal Name: RICERCHE DI MATEMATICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.2653-2659
  • Keywords: Finite groups, Real characters, Strongly monolithic characters, Zeros of irreducible characters
  • Istanbul University Affiliated: Yes

Abstract

In this paper, we are interested in the real-valued strongly monolithic characters of finite groups. We give some criteria for solvability and normal p-complements of finite groups by their real-valued strongly monolithic characters. We also prove that a finite nonsolvable group has a real-valued strongly monolithic character of degree >= 5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\geqslant 5$$\end{document}. Additionally, we give a classification for odd-square-free groups by using their real-valued strongly monolithic characters and the zeros of their irreducible characters of odd degree.