Kleidman, Peter B.; Ryba, A. J. E. Kostant’s conjecture holds for \(E_ 7\): \(L_ 2(37)<E_ 7(\mathbb{C})\). (English) Zbl 0839.20023 J. Algebra 161, No. 2, 535-540 (1993). Let \(G\) be an adjoint group of Lie-type over \(\mathbb{C}\) with Coxeter number \(h\). Kostant’s conjecture runs as follows: if \(2h+1\) is a prime power, then \(L_2 (2h+1) <G\) [see A. M. Cohen and R. L. Griess, Proc. Symp. Pure Math. 47, 367-405 (1987; Zbl 0654.22005)]. Taking the known results into account, to settle Kostant’s conjecture, it remains to determine whether \(L_2 (37)\) is contained in \(E_7 (\mathbb{C})\) and whether \(L_2(61)\) is contained in \(E_8 (\mathbb{C})\). In this note the authors report on their computer research, which establishes the conjecture for \(E_7\). Reviewer: V.M.Levchuk (Krasnoyarsk) Cited in 5 Documents MSC: 20D06 Simple groups: alternating groups and groups of Lie type 20G20 Linear algebraic groups over the reals, the complexes, the quaternions 20E07 Subgroup theorems; subgroup growth Keywords:finite simple subgroups of \(E_ 7(\mathbb{C})\); adjoint groups of Lie-type; Coxeter number; Kostant conjecture Citations:Zbl 0654.22005 PDFBibTeX XMLCite \textit{P. B. Kleidman} and \textit{A. J. E. Ryba}, J. Algebra 161, No. 2, 535--540 (1993; Zbl 0839.20023) Full Text: DOI