Classes of Finite Groups,9781402047183

Classes of Finite Groups

by ;
ISBN13: 9781402047183
ISBN10: 1402047185
Format: Hardcover
Pub. Date: 2006-07-15
Publisher(s): Springer Nature
List Price: $149.99

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Summary

Many group theorists all over the world have been trying in the last twenty-five years to extend and adapt the magnificent methods of the Theory of Finite Soluble Groups to the more ambitious universe of all finite groups. This is a natural progression after the classification of finite simple groups but the achievements in this area are scattered in various papers. Our objectives in this book were to gather, order and examine all this material, including the latest advances made, give a new approach to some classic topics, shed light on some fundamental facts that still remain unpublished and present some new subjects of research in the theory of classes of finite, not necessarily solvable, groups.

Table of Contents

Preface ix
1 Maximal subgroups and chief factors 1(86)
1.1 Primitive groups
1(39)
1.2 A generalisation of the Jordan-Holder theorem
40(22)
1.3 Crowns
62(11)
1.4 Systems of maximal subgroups
73(14)
2 Classes of groups and their properties 87(38)
2.1 Classes of groups and closure operators
87(4)
2.2 Formations: Basic properties and results
91(7)
2.3 Schunck classes and projectors
98(11)
2.4 Fitting classes, Fitting sets, and injectors
109(9)
2.5 Fitting formations
118(7)
3 Χ-local formations 125(44)
3.1 Χ-local formations
126(18)
3.2 A generalisation of Gaschütz-Lubeseder-Schmid-Baer theorem
144(9)
3.3 Products of χ-local formations
153(10)
3.4 ω-local formations
163(6)
4 Normalisers and prefrattini subgroups 169(36)
4.1 -normalisers
171(8)
4.2 Normalisers of groups with soluble residual
179(11)
4.3 Subgroups of prefrattini type
190(15)
5 Subgroups of soluble type 205(30)
5.1 Subgroup functors and subgroups of soluble type: elementary properties
206(9)
5.2 Existence criteria
215(9)
5.3 Projectors of soluble type
224(11)
6 -subnormality 235(74)
6.1 Basic properties
235(4)
6.2 -subnormal closure
239(8)
6.3 Lattice formations
247(18)
6.4 -subnormal subgroups and -critical groups
265(20)
6.5 Wielandt operators
285(24)
7 Fitting classes and injectors 309(46)
7.1 A non-injective Fitting class
309(6)
7.2 Injective Fitting classes
315(14)
7.3 Supersoluble Fitting classes
329(10)
7.4 Fitting sets, Fitting sets pairs, and outer Fitting sets pairs
339(16)
References 355(12)
List of symbols 367(4)
Index of authors 371(4)
Index 375

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