The overgroups of the solvable subgroup of maximal order in \(S_ n\)
\textit{A. Mann} [Isr. J. Math. 55, 162-172 (1986; Zbl 0609.20015)] determined the solvable subgroups of maximal order in the symmetric group \(S_ n\). In this note the structure of the overgroups of such subgroups is given. In his Ph. D. Thesis the author stated that the Borel subgroup of a finite simple group of Lie type can be characterized as the solvable subgroup of maximal order (excluded the groups defined over the fields of order 2, 3, 5 and 7), therefore the appropriate overgroups in the finite simple groups of Lie type over the fields of sufficiently large orders are the parabolic subgroups.
scientific article; zbMATH DE number 4107070
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