SOME CRITERIA FOR SOLVABILITY AND NILPOTENCY OF FINITE GROUPS BY STRONGLY MONOLITHIC CHARACTERS


Gungor S. B., ERKOÇ T.

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, vol.108, no.1, pp.120-124, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 108 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.1017/s0004972722000958
  • Journal Name: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.120-124
  • Istanbul University Affiliated: Yes

Abstract

Gagola and Lewis ['A character theoretic condition characterizing nilpotent groups', Comm. Algebra27 (1999), 1053-1056] proved that a finite group G is nilpotent if and only if chi(1)(2) divides vertical bar G:ker chi vertical bar for every irreducible character chi of G. The theorem was later generalised by using monolithic characters. We generalise the theorem further considering only strongly monolithic characters. We also give some criteria for solvability and nilpotency of finite groups by their strongly monolithic characters.