A lattice theoretic characterization for the existence of a faithful irreducible representation (Q6618055)

Let \(G\) be a finite group. \textit{S. Palcoux}, in [J. Algebra 505, 279--287 (2018; Zbl 1437.20017)], proved the following result: if \(G\) contains a core-free subgroup H such that the interval \(\mathrm{Int}(H, H^{\ast})\) in the subgroup lattice of \(G\) is Boolean, then \(G\) has a faithful irreducible complex representation.\N\NIn the paper under review, the author proves the converse of the previous statement. So, Palcoux's condition is necessary and sufficient.