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Structure Theory for Canonical Classes of Finite Groups 2015 ed. [Kõva köide]

  • Formaat: Hardback, 359 pages, kõrgus x laius: 235x155 mm, kaal: 729 g, XIV, 359 p., 1 Hardback
  • Ilmumisaeg: 08-May-2015
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3662457466
  • ISBN-13: 9783662457467
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Structure Theory for Canonical Classes of Finite Groups 2015 ed.Suurem pilt
  • Formaat: Hardback, 359 pages, kõrgus x laius: 235x155 mm, kaal: 729 g, XIV, 359 p., 1 Hardback
  • Ilmumisaeg: 08-May-2015
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3662457466
  • ISBN-13: 9783662457467
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783662457467.html
Märksõnad:

This book offers a systematic introduction to recent achievements and development in research on the structure of finite non-simple groups, the theory of classes of groups and their applications. In particular, the related systematic theories are considered and some new approaches and research methods are described – e.g., the F-hypercenter of groups, X-permutable subgroups, subgroup functors, generalized supplementary subgroups, quasi-F-group, and F-cohypercenter for Fitting classes. At the end of each chapter, we provide relevant supplementary information and introduce readers to selected open problems.

Arvustused

The book under review aims to be a continuation of these references and to analyze, systematize and report about subsequent developments in the theory of finite groups. A section at the end of each chapter includes additional related information and open problems. The book is addressed to people familiar with the theory of classes of groups and certainly of interest for researchers in this area of research. (M. Dolores Pérez-Ramos, Mathematical Reviews, June, 2016)

The interested reader of this book is the specialist of general structure theory of groups, who will find a great number of results easily accessible in a unified presentation ready for deeper study, so far accessible only scattered in original research papers. The author boldly undertook and has successfully completed the task of presenting the diversified researchmethods and results, combining the application oriented approach with inviting exposition and pertinent examples. (János Kurdics, zbMATH 1343.20021, 2016)

1 The Hypercenter and Its Generalizations
1(62)
1.1 Basic Concepts and Results
1(6)
1.2 Generalized Hypercentral Subgroups
7(13)
1.3 The Theory of Quasi-Groups
20(15)
1.4 On Factorizations of Groups with hypercentral Intersections of the Factors
35(7)
1.5 The Intersection of maximal Subgroups
42(16)
1.6 Additional Information and Some Problems
58(5)
2 Groups With Given Systems of X-Permutable Subgroups
63(66)
2.1 Base Concepts
63(8)
2.2 Criterions of Existence and Conjugacy of Hall Subgroups
71(13)
2.3 On the Groups in Which Every Subgroup Can be Written as an Intersection of Some Subgroups of Prime Power Indices
84(7)
2.4 Criteria of Supersolubility and p-Supersolubility for Products of Groups
91(8)
2.5 Characterizations of Classes of Groups in Terms of X-Permutable Subgroups
99(24)
2.6 Additional Information and Some Problems
123(6)
3 Between Complement and Supplement
129(62)
3.1 Base Concepts and Lemmas
130(11)
3.2 Base Theorems
141(26)
3.3 Groups with Some Special Supplement Conditions for Subgroups
167(15)
3.4 G-covering Systems of Subgroups
182(6)
3.5 Additional Information and Some Problems
188(3)
4 Groups With Given Maximal Chains of Subgroups
191(58)
4.1 Σ-Embedded Subgroups
191(10)
4.2 Groups with Permutability for 2-Maximal and 3-Maximal Subgroups
201(25)
4.3 Finite Groups of Spencer Height ≤ 3
226(5)
4.4 On θ-Pairs for Maximal Subgroups of a Finite Group
231(12)
4.5 Additional Information and Some Problems
243(6)
5 Formations and Fitting Classes
249(88)
5.1 Generated ω-Composition and ω-Local Formations
249(3)
5.2 The Criterion of ω-Compositively of the First Factor of One-Generated ω-Composition Product of Two Formations
252(6)
5.3 Noncancellative Factorizations of One-Generated ω-Composition Formations
258(15)
5.4 On Two Problems of the Lattice Theory of Formations
273(18)
5.5 On a Question of the Theory of Graduated Formation
291(5)
5.6 Injectors and Covering Subgroups
296(13)
5.7 Classes Determined by Hall Subgroups
309(8)
5.8 The Theory of Cocentrality of Chief Factors and Cohypercenter for Fitting Classes
317(7)
5.9 On ω-Local Fitting Classes and Lockett Conjecture
324(6)
5.10 A Problem Concerning the Residuals of Groups
330(2)
5.11 Additional Information and Some Problems
332(5)
Bibliography 337(18)
List of Symbols 355(2)
Index of Subjects 357