1 results
SOME CRITERIA FOR SOLVABILITY AND NILPOTENCY OF FINITE GROUPS BY STRONGLY MONOLITHIC CHARACTERS
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society / Volume 108 / Issue 1 / August 2023
- Published online by Cambridge University Press:
- 22 September 2022, pp. 120-124
- Print publication:
- August 2023
-
- Article
- Export citation
-
Gagola and Lewis [‘A character theoretic condition characterizing nilpotent groups’, Comm. Algebra 27 (1999), 1053–1056] proved that a finite group G is nilpotent if and only if
$\chi (1)^{2}$ divides 
$\lvert G:\textrm {ker}\,\chi \rvert $ 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.
