UID:
edoccha_9961612701402883
Format:
1 online resource (303 pages)
Edition:
1st ed.
ISBN:
9783031629150
Series Statement:
Lecture Notes in Mathematics Series ; v.2346
Note:
Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Introduction and Historical Background -- 1.2 Basic Notation and Terminology -- 1.3 Reduction to Linear Groups -- 2 Basic Structure of Maximal Irreducible Solvable Subgroups -- 2.1 Construction of Maximal Irreducible Solvable Groups -- 2.1.1 General Setup and Notation -- 2.1.2 Generalities on Maximal Solvable Subgroups -- 2.1.3 Representation Theory -- 2.1.4 Number Theory -- 2.2 Metrically Imprimitive Subgroups -- 2.3 Metrically Completely Reducible Subgroups -- 2.4 Metrically Primitive Maximal Irreducible Solvable Subgroups -- 2.5 Groups of Type B_0 -- 2.6 Groups of Type B_1 -- 2.7 Groups of Type B_2 -- 2.8 Groups of Type B_3 -- 2.9 Groups of Type B_i with μ = 1 -- 3 Extraspecial Groups -- 3.1 Extraspecial Groups -- 3.2 Absolutely Irreducible Representations of Extraspecial Groups -- 3.2.1 Absolutely Irreducible Representation of r+1+2 -- 3.2.2 Unitary Representation of r+1+2 -- 3.2.3 Orthogonal Representation of 2+1+2 -- 3.2.4 Absolutely Irreducible Representation of 2-1+2 -- 3.2.5 Unitary Representation of 2-1+2 -- 3.2.6 Symplectic Representation of 2-1+2 -- 4 Metrically Primitive Maximal Irreducible Solvable Subgroups -- 4.1 The Fitting Subgroup of C_G(F_0) -- 4.2 Structure of Metrically Primitive Maximal Solvable Subgroups -- 4.3 Description of Gμ,νB(X1, …, Xk) -- 4.3.1 Groups of Type B0 -- 4.3.2 Groups of Type B1 -- 4.3.3 Groups of Type B2 -- 4.3.4 Groups of Type B3 -- 4.3.5 General Properties of Gμ,νB(X1, …, Xk) -- 4.4 Maximal Irreducible Solvable Subgroups of GO(n,q) for n Odd -- 5 Basic Properties of Gμ,νB(X1, …, Xk) -- 5.1 Maximal Irreducible Solvable Subgroups of Multiplier 2 -- 5.2 Irreducibility of Gμ,νB(X1, …, Xk) -- 5.3 Properties of F_0 and A in Gμ,νB(X1, …, Xk) -- 5.4 Examples of the Construction in Some Special Cases.
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5.5 Some Examples Where Gμ,νB(X1, …, Xk) Is Not Maximal Solvable -- 5.6 Primitivity of Gμ,νB(X1, …, Xk) -- 5.7 Uniqueness of F_0 and A -- 5.8 Conjugacy of Gμ,νB(X1, …, Xk) -- 6 Fixed Point Spaces and Abelian Subgroups -- 6.1 Fixed Point Spaces in Symplectic-Type Normalizers -- 6.2 Fixed Point Spaces in Primitive Solvable Linear Groups -- 6.3 Abelian Subgroups of Solvable Affine Groups -- 7 Maximality of the Groups Constructed -- 7.1 Maximality of G(X_1, ..., X_k) -- 7.2 Completely Reducible Subgroups of G(X_1, …, X_k) -- 7.3 Systems of Imprimitivity for Completely Reducible Subgroups -- 7.4 Maximality of Metrically Imprimitive Subgroups -- 7.5 Maximality of Metrically Completely Reducible Subgroups -- 7.6 Further Results -- 8 Examples -- 8.1 Examples and Summary of Construction -- 8.2 Tables of Examples -- References -- Index.
Additional Edition:
Print version: Korhonen, Mikko Maximal Solvable Subgroups of Finite Classical Groups Cham : Springer,c2024 ISBN 9783031629143
Language:
English
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