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  • © 1956

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

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Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (MATHE2, volume 10)

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  • ISBN: 978-3-642-52758-6
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Table of contents (5 chapters)

  1. Front Matter

    Pages i-vii
  2. Introduction

    • Michio Suzuki
    Pages 1-2
  3. Isomorphisms of subgroup lattices

    • Michio Suzuki
    Pages 31-57
  4. Homomorphisms of subgroup lattices

    • Michio Suzuki
    Pages 57-85
  5. Dualisms of subgroup lattices

    • Michio Suzuki
    Pages 85-92
  6. Back Matter

    Pages 92-96

About this book

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 To obtain a systematic treatment of the subject quite a few unpublished results of the author had to be included.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 someĀ­ 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

  • Book Title: Structure of a Group and the Structure of its Lattice of Subgroups

  • Authors: Michio Suzuki

  • Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge

  • DOI: https://doi.org/10.1007/978-3-642-52758-6

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1956

  • Softcover ISBN: 978-3-642-52760-9

  • eBook ISBN: 978-3-642-52758-6

  • Edition Number: 1

  • Number of Pages: VIII, 96

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Group Theory and Generalizations

Buying options

eBook USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-3-642-52758-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 84.99
Price excludes VAT (USA)