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Description of  Maximal Solvable Subgroups of Finite Classical Groups (Lecture Notes in Mathematics)

3031629140 pdf This book studies maximal solvable subgroups of classical groups over finite fields. It provides the first modern account of Camille Jordan's classical results, and extends them, giving a classification of maximal irreducible solvable subgroups of general linear groups, symplectic groups, and orthogonal groups over arbitrary finite fields. A subgroup of a group G is said to be maximal solvable if it is maximal among the solvable subgroups of G. The history of this notion goes back to Jordans Trait (1870), in which he provided a classification of maximal solvable subgroups of symmetric groups. The main difficulty is in the primitive case, which leads to the problem of classifying maximal irreducible solvable subgroups of general linear groups over a field of prime order. One purpose of this monograph is expository: to give a proof of Jordans classification in modern terms. More generally, the aim is to generalize these results to classical groups over arbitrary finite fields, and to provide other results of interest related to irreducible solvable matrix groups. Read more