2 edition of **On the theory of fitting classes of finite soluble groups.** found in the catalog.

On the theory of fitting classes of finite soluble groups.

Elspeth Lynn Cusack

- 57 Want to read
- 28 Currently reading

Published
**1979**
by University of East Anglia in Norwich
.

Written in English

**Edition Notes**

Thesis (Ph.D.) - University of East Anglia, School of Mathematics and Physics, 1979.

ID Numbers | |
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Open Library | OL13845922M |

Chapter VI. Further theory of Schunck classes; Chapter VII. Further theory of formations; Chapter VIII. Injectors and Fitting sets; Chapter IX. Fitting classes — examples and properties related to injectors; Chapter X. Fitting classes — the Lockett section; Chapter XI. Fitting classes — their behaviour as classes of groups; Appendix α. A. Finite Soluble Groups. Series:De Gruyter Expositions in Mathematics 4. ,00 Further theory of Schunck classes. Pages Get Access to Full Text. Chapter VII. Injectors and Fitting sets. Pages Get Access to Full Text. Chapter IX. Fitting classes — examples and properties related to injectors. Pages Get Access.

Here we present our contributions, embedded in a survey of the progress so far made in this tantalizing part of finite soluble group theory. Chapter 0 indicates the group theoretic notation we use, while Chapter 1 contains the basic results and terminology of Fitting class by: J. Group Theory 6 (), (de Gruyter Stephanie Rei¤erscheid (Communicated by C. W. Parker) 1 Introduction The subgroup-closure of a Fitting class of finite soluble groups is strong enough to guarantee the closure of the class under a number of further closure operations; this was proved in by Bryce and Cossey (cf. [1], [3]). More precisely they showed .

AbstractIn this paper we are concerned with finite soluble groups G admitting a factorisation G=AB${G=AB}$, with A and B proper subgroups having coprime order. We are interested in bounding the Fitting height of G in terms of some group-invariants of A and B, including the Fitting heights and the derived by: 8. solvable groups all of whose 2-local subgroups are solvable. The reader will realize that nearly all of the methods and results of this book are used in this investigation. At least two things have been excluded from this book: the representation theory of ﬁnite groups and—with a few exceptions—the description of the ﬁnite simple Size: 1MB.

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On the theory of Fitting classes of finite soluble groups F. Peter Lockett 1 Mathematische Zeitschrift volumepages – () Cite this articleCited by: 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. Classes of Finite Groups. 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. This book covers the latest achievements of the Theory of Classes of Finite Groups.

By gathering the research of many authors scattered in hundreds of papers the book contributes to the understanding of the structure of finite groups by adapting and extending the successful techniques of the Theory of Finite Soluble Groups. On the theory of fitting classes of finite soluble groups.

By Francis Peter Lockett. Get PDF (5 MB) Abstract. We continue the study Fitting classes begun by Fischer in\ud and carried on by (notably) Gaschütz and Hartley.\ud Disappointingly the theory has, as yet, failed to display the\ud richness of its predecessor, the theory of Author: Francis Peter Lockett.

This book covers the latest achievements of the Theory of Classes of Finite Groups. "The authors of the book under review aim to collect what can be said in the same way about finite groups, soluble or not.

The book is very helpful for the 5 Subgroups of soluble type -- 6 F-subnormality -- 7 Fitting classes and injectors. Peter Lockett, "On the theory of Fitting classes of finite soluble groups", (PhD thesis, University of Warwick, Coventry, ).

zbMATH Google Scholar [38] F. Peter Lockett, "On the theory of Fitting classes of finite soluble groups", Math. (), –Cited by: 9. Abstract. I want to give here a rather biased account of recent work in the theory of classes of finite soluble groups.

I will be concentrating on results which have something to say about the classes themselves, rather than results which use the classes to obtain a picture of the internal structure of finite soluble by: 9.

Download Citation | Structure Theory for Canonical Classes of Finite Groups | This book offers a systematic introduction to recent achievements and development in research on the structure of.

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.

Sylow Theory, Formations and Fitting Classes in Locally Finite Groups. This book is concerned with the generalizations of Sylow theorems and the related topics of formations and the fitting of classes to locally finite groups. We continue the study Fitting classes begun by Fischer in and carried on by (notably) Gaschütz and Hartley.

Disappointingly the theory has, as yet, failed to display the richness of its predecessor, the theory of Formations. Here we present our contributions, embedded in a survey of the progress so far made in this tantalizing part of finite soluble group theory.

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.5/5(1).

About this book Introduction 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.

The theory of infinite soluble groups has developed in directions quite different from the older theory of finite soluble groups. A noticeable feature of the infinite theory is the strong interaction with commutative algebra, which is due to the role played by the group ring.

Despite this fact the exposition that follows is largely by: 7. Finite Soluble Groups. The aim of the Expositions is to present new and important developments in pure and applied mathematics.

Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics.

Classes of Finite Groups (Mathematics and Its Applications) Hardcover – July 11 "The authors of the book under review aim to collect what can be said in the same way about finite groups, soluble or not.

The book is very helpful for the reader to obtain information on recent results, a valuable source for anybody doing research in this Cited by: Finite Soluble Groups.

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics.

From recent results of Lausch, it is easy to establish necessary and sufficient conditions for a Fitting class to be maximal in the class of all finite soluble groups.

Let X, F, X ⊆ F, be non-trivial Fitting classes of finite soluble groups such that G X is an X-injector of G for all G∈ X is said to be normal in F (F-normal).We show that for a subgroup-closed Fitting class X the collection of all subgroup-closed Fitting classes in which X is normal forms a complete, distributive and atomic lattice.

Moreover, X is determined uniquely by the unique Cited by: 1. 3. Normal Fitting classes. 4. The Lausch group.

5. Examples of Fitting pairs and Berger's theorem. 6. The Lockett conjecture --Ch. XI. Fitting classes --their behaviour as classes of groups.

1. Fitting formations. 2. Metanilpotent Fitting classes with additional closure properties. 3. Further theory of metanilpotent Fitting classes. 4.A Fitting class FF is called dominant in the class of all finite soluble groups SS if F⊆SF⊆S and for every group G∈SG∈S any two FF-maximal subgroups of G containing the FF-radical GFGF of.Geometric Group Theory Preliminary Version Under revision.

The goal of this book is to present several central topics in geometric group theory, primarily related to the large scale geometry of infinite groups and spaces on which such groups act, and to illustrate them with fundamental theorems such as Gromov’s Theorem on groups of polynomial growth.