A lattice theoretic characterization for the existence of a faithful irreducible representation

Document Type : Ischia Group Theory 2022

Author

Alfréd Rényi Institute of Mathematics, P.O.Box 127, 1364 Budapest, Hungary

Abstract

In a recent article S'ebastien Palcoux formulated a sufficient condition on the subgroup lattice of a finite group $G$ that guarantees the existence of a faithful irreducible complex representation of $G$, and asked whether his condition is also necessary. In this short note we give an affirmative answer using Kochend\"orffer's criterion for the existence of a faithful irreducible representation based on the structure of the socle of $G$.

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Main Subjects


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Volume 13, Issue 4 - Serial Number 4
Proceedings of the Ischia Group Theory 2022-Part I
December 2024
Pages 345-350
  • Receive Date: 27 July 2023
  • Revise Date: 27 August 2023
  • Accept Date: 23 August 2023
  • Published Online: 30 August 2023