The Theory of Nilpotent Groups
The Theory of Nilpotent Groups

Author: Anthony E. Clement

Publisher: Birkhäuser

Published: 2017-11-18

Total Pages: 318

ISBN-13: 3319662139

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This monograph presents both classical and recent results in the theory of nilpotent groups and provides a self-contained, comprehensive reference on the topic. While the theorems and proofs included can be found throughout the existing literature, this is the first book to collect them in a single volume. Details omitted from the original sources, along with additional computations and explanations, have been added to foster a stronger understanding of the theory of nilpotent groups and the techniques commonly used to study them. Topics discussed include collection processes, normal forms and embeddings, isolators, extraction of roots, P-localization, dimension subgroups and Lie algebras, decision problems, and nilpotent groups of automorphisms. Requiring only a strong undergraduate or beginning graduate background in algebra, graduate students and researchers in mathematics will find The Theory of Nilpotent Groups to be a valuable resource.

Finiteness Conditions and Generalized Soluble Groups
Finiteness Conditions and Generalized Soluble Groups

Author: Derek J.S. Robinson

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 269

ISBN-13: 3662117479

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This book is a study of group theoretical properties of two disparate kinds, firstly finiteness conditions or generalizations of finiteness and secondly generalizations of solubility or nilpotence. It will be particularly interesting to discuss groups which possess properties of both types. The origins of the subject may be traced back to the nineteen twenties and thirties and are associated with the names of R. Baer, S.N. Cernikov, K.A. Hirsch, A.G. Kuros, 0.]. Schmidt and H. Wielandt. Since this early period, the body of theory has expanded at an increasingly rapid rate through the efforts of many group theorists, particularly in Germany, Great Britain and the Soviet Union. Some of the highest points attained can, perhaps, be found in the work of P. Hall and A.I. Mal'cev on infinite soluble groups. Kuras's well-known book "The theory of groups" has exercised a strong influence on the development of the theory of infinite groups: this is particularly true of the second edition in its English translation of 1955. To cope with the enormous increase in knowledge since that date, a third volume, containing a survey of the contents of a very large number of papers but without proofs, was added to the book in 1967

Localization of Nilpotent Groups and Spaces
Localization of Nilpotent Groups and Spaces

Author: Peter Hilton

Publisher: Elsevier

Published: 2016-06-03

Total Pages: 167

ISBN-13: 1483258742

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North-Holland Mathematics Studies, 15: Localization of Nilpotent Groups and Spaces focuses on the application of localization methods to nilpotent groups and spaces. The book first discusses the localization of nilpotent groups, including localization theory of nilpotent groups, properties of localization in N, further properties of localization, actions of a nilpotent group on an abelian group, and generalized Serre classes of groups. The book then examines homotopy types, as well as mixing of homotopy types, localizing H-spaces, main (pullback) theorem, quasifinite nilpotent spaces, localization of nilpotent complexes, and nilpotent spaces. The manuscript takes a look at the applications of localization theory, including genus and H-spaces, finite H-spaces, and non-cancellation phenomena. The publication is a vital source of data for mathematicians and researchers interested in the localization of nilpotent groups and spaces.

Finiteness Conditions and Generalized Soluble Groups
Finiteness Conditions and Generalized Soluble Groups

Author: Derek John Scott Robinson

Publisher: Springer

Published: 1972

Total Pages: 236

ISBN-13:

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This book is a study of group theoretical properties of two disparate kinds, firstly finiteness conditions or generalizations of finiteness, and secondly generalizations of solubility or nilpotence. Particularly interesting are the groups which possess properties of both types. This volume collects the most important results in the theory, to present them in a compact and accessible form with improved and shortened proofs wherever possible. Readers should have a good basic knowledge of group theory, Abelian groups, and the more familiar parts of commutative algebra and ring theory.

Crystallographic Groups and Their Generalizations
Crystallographic Groups and Their Generalizations

Author: Paul Igodt

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 330

ISBN-13: 082182001X

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This volume contains articles written by the invited speakers and workshop participants from the conference on "Crystallographic Groups and Their Generalizations", held at Katholieke Universiteit Leuven, Kortrijk (Belgium). Presented are recent developments and open problems. Topics include the theory of affine structures and polynomial structures, affine Schottky groups and crooked tilings, theory and problems on the geometry of finitely generated solvable groups, flat Lorentz 3-manifolds and Fuchsian groups, filiform Lie algebras, hyperbolic automorphisms and Anosov diffeomorphisms on infra-nilmanifolds, localization theory of virtually nilpotent groups and aspherical spaces, projective varieties, and results on affine appartment systems. Participants delivered high-level research mathematics and a discussion was held forum for new researchers. The survey results and original papers contained in this volume offer a comprehensive view of current developments in the field.