Karl Strambach's Books

Algebraic Groups and Lie Groups with Few Factors

By: Alfonso Di Bartolo,Giovanni Falcone,Peter Plaumann,Karl Strambach

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Algebraic Groups and Lie Groups with Few Factors

By: Alfonso Di Bartolo,Giovanni Falcone,Peter Plaumann,Karl Strambach

Algebraic groups are treated in this volume from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups. The main body of the text is devoted to a classification of algebraic groups and Lie groups having only few subgroups or few factor groups of different type. In particular, the diversity of the nature of algebraic groups over fields of positive characteristic and over fields of characteristic zero is emphasized. This is revealed by the plethora of three-dimensional unipotent algebraic groups over a perfect field of positive characteristic, as well as, by many concrete examples which cover an area systematically. In the final section, algebraic groups and Lie groups having many closed normal subgroups are determined.

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Page Count

223

Publisher

Springer

Published Date

ISBN 10

3540785841

ISBN 13

9783540785842

Loops in Group Theory and Lie Theory

By: Péter Nagy,Karl Strambach

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Loops in Group Theory and Lie Theory

By: Péter Nagy,Karl Strambach

In this book the theory of binary systems is considered as a part of group theory and, in particular, within the framework of Lie groups. The novelty is the consequent treatment of topological and differentiable loops as topological and differentiable sections in Lie groups. The interplay of methods and tools from group theory, differential geometry and topology, symmetric spaces, topological geometry, and the theory of foliations is what gives a special flavour to the results presented in this book. It is the first monograph devoted to the study of global loops. So far books on differentiable loops deal with local loops only. This theory can only be used partially for the theory of global loops since non-associative local structures have, in general, no global forms. The text is addressed to researchers in non-associative algebra and foundations of geometry. It should prove enlightening to a broad range of readers, including mathematicians working in group theory, the theory of Lie groups, in differential and topological geometry, and in algebraic groups. The authors have produced a text that is suitable not only for a graduate course, but also for selfstudy in the subjectby interested graduate students. Moreover, the material presented can be used for lectures and seminars in algebra, topological algebra and geometry.

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Page Count

377

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110900580

ISBN 13

9783110900583

Periodic Locally Compact Groups

A Study of a Class of Totally Disconnected Topological Groups

By: Wolfgang Herfort,Karl H. Hofmann,Francesco G. Russo

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Periodic Locally Compact Groups

A Study of a Class of Totally Disconnected Topological Groups

By: Wolfgang Herfort,Karl H. Hofmann,Francesco G. Russo

This authoritative book on periodic locally compact groups is divided into three parts: The first part covers the necessary background material on locally compact groups including the Chabauty topology on the space of closed subgroups of a locally compact group, its Sylow theory, and the introduction, classifi cation and use of inductively monothetic groups. The second part develops a general structure theory of locally compact near abelian groups, pointing out some of its connections with number theory and graph theory and illustrating it by a large exhibit of examples. Finally, the third part uses this theory for a complete, enlarged and novel presentation of Mukhin’s pioneering work generalizing to locally compact groups Iwasawa’s early investigations of the lattice of subgroups of abstract groups. Contents Part I: Background information on locally compact groups Locally compact spaces and groups Periodic locally compact groups and their Sylow theory Abelian periodic groups Scalar automorphisms and the mastergraph Inductively monothetic groups Part II: Near abelian groups The definition of near abelian groups Important consequences of the definitions Trivial near abelian groups The class of near abelian groups The Sylow structure of periodic nontrivial near abelian groups and their prime graphs A list of examples Part III: Applications Classifying topologically quasihamiltonian groups Locally compact groups with a modular subgroup lattice Strongly topologically quasihamiltonian groups

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Page Count

457

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110599082

ISBN 13

9783110599084

The Structure of Compact Groups

A Primer for the Student – A Handbook for the Expert

By: Karl H. Hofmann,Sidney A. Morris

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The Structure of Compact Groups

A Primer for the Student – A Handbook for the Expert

By: Karl H. Hofmann,Sidney A. Morris

This book is designed both as a textbook for high-level graduate courses and as a reference for researchers who need to apply the structure and representation theory of compact groups. A gentle introduction to compact groups and their representation theory is followed by self-contained courses on linear and compact Lie groups, and on locally compact abelian groups. This fourth edition was updated with the latest developments in the field.

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Page Count

1398

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3110696010

ISBN 13

9783110696011

Loops in Group Theory and Lie Theory

By: Péter Nagy,Karl Strambach

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Loops in Group Theory and Lie Theory

By: Péter Nagy,Karl Strambach

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Solve jigsaw puzzle

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Page Count

377

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110900580

ISBN 13

9783110900583

Book's by Karl Strambach

Algebraic Groups and Lie Groups with Few Factors

Algebraic Groups and Lie Groups with Few Factors

Loops in Group Theory and Lie Theory

Loops in Group Theory and Lie Theory

Periodic Locally Compact Groups

Periodic Locally Compact Groups

The Structure of Compact Groups

The Structure of Compact Groups

Loops in Group Theory and Lie Theory

Loops in Group Theory and Lie Theory

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