Structure of a Group and the Structure of its Lattice of Subgroups

  • Authors
  • Michio¬†Suzuki

Part of the Ergebnisse der Mathematik und Ihrer Grenzgebiete book series (MATHE2, volume 10)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Michio Suzuki
    Pages 1-2
  3. Michio Suzuki
    Pages 31-57
  4. Michio Suzuki
    Pages 57-85
  5. Michio Suzuki
    Pages 85-92
  6. Back Matter
    Pages 92-96

About these proceedings

Introduction

The central theme of this monograph is the relation between the structure of a group and the structure of its lattice of subgroups. Since the first papers on this topic have appeared, notably those of BAER and ORE, a large body of literature has grown up around this theory, and it is our aim to give a picture of the present state of this theory. To obtain a systematic treatment of the subject quite a few unpublished results of the author had to be included. On the other hand, it is natural that we could not reproduce every detail and had to treat some parts some­ wh at sketchily. We have tried to make this report as self-contained as possible. Accordingly we have given some proofs in considerable detail, though of course it is in the nature of such areport that many proofs have to be omitted or can only be given in outline. Similarly references to the concepts and theorems used are almost exclusively references to standard works like BIRKHOFF [lJ and ZASSENHAUS [lJ. The author would like to express his sincere gratitude to Professors REINHOLD BAER and DONALD G. HIGMAN for their kindness in giving hirn many valuable suggestions. His thanks are also due to Dr. NOBORU ITo who, during stimulating conversations, contributed many useful ideas. Urbana, May, 1956. M. Suzuki. Contents.

Keywords

Abelian group Etch Lattice Natural boundary element method finite group group proof sketch theorem

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-52758-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1956
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-52760-9
  • Online ISBN 978-3-642-52758-6
  • Series Print ISSN 0071-1136
  • About this book