Finiteness Conditions and Generalized Soluble Groups: Part 1

✍ Scribed by Derek J. S. Robinson (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1972
• Tongue: English
• Leaves: 225
• Series: Ergebnisse der Mathematik und ihrer Grenzgebiete 62
• Edition: 1
• Category: Library

✦ Synopsis

This book is a study of group theoretical properties of two dis­ parate kinds, firstly finiteness conditions or generalizations of fini­ teness 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. Wie­ landt. 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.

✦ Table of Contents

Front Matter....Pages I-XV
Fundamental Concepts in the Theory of Infinite Groups....Pages 1-41
Soluble and Nilpotent Groups....Pages 42-64
Maximal and Minimal Conditions....Pages 65-100
Finiteness Conditions on Conjugates and Commutators....Pages 101-142
Finiteness Conditions on the Normal and Subnormal Structure of a Group....Pages 143-186
Back Matter....Pages 187-212

✦ Subjects

Mathematics, general