CBMS Regional Conference Series in Mathematics
Volume: 33; 1977; 74 pp; Softcover
MSC: Primary 20;
Print ISBN: 978-0-8218-1683-7
Product Code: CBMS/33
List Price: $27.00
Individual Price: $21.60

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Electronic ISBN: 978-1-4704-2393-3
Product Code: CBMS/33.E
List Price: $27.00
Individual Price: $21.60

Factorizations in Local Subgroups of Finite Groups

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G. Glauberman

A co-publication of the AMS and CBMS

This monograph focuses on progress in the study of Sylow subgroups and their influence on the structure of the group as a whole. This research has been applied to other areas of finite group theory, including classification of simple groups, but is also of independent interest and does not require extensive background or long proofs.

In 1969, the author gave a report on this topic which appeared in the book Finite simple groups (edited by M. B. Powell and G. Higman, Academic Press, 1971; MR 48 #6228). The present monograph covers progress since 1969. It includes some new results of Yoshida on transfer, a partial analogue for $p-2$ of the author's “$ZJ$-Theorem”, and the classification of all simple groups which are $S^4$-free, i.e., in which the symmetric group of degree four is not involved. It also includes an expository account of recent work of M. Aschbacher, B. Baumann, R. Niles, and others on “failure of factorization”, “pushing-up” arguments, and related subjects.

This is not an expository work. This work should be accessible to advanced graduate students. In particular, a semester's study in finite group theory beyond the M.A. or M.S. degree should be adequate background, e.g., Chapters 1–3 and 5–7 of Gorenstein's Reviews on finite groups (Amer. Math. Soc., 1974; MR 50 #2312). The book supplements the author's report in Finite simple groups. Familarity with this report is recommended but not assumed.

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Factorizations in Local Subgroups of Finite Groups

Base Product Code Keyword List: cbms; CBMS; cbms/33; CBMS/33; cbms-33; CBMS-33

Print Product Code: CBMS/33

Online Product Code: CBMS/33.E

Title (HTML): Factorizations in Local Subgroups of Finite Groups

Author(s) (Product display): G. Glauberman

Publisher Blurb: A co-publication of the AMS and CBMS

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Book Series Name: CBMS Regional Conference Series in Mathematics

Volume: 33

Publication Month and Year: 1977-12-31

Page Count: 74

Cover Type: Softcover

Print ISBN-13: 978-0-8218-1683-7

Online ISBN 13: 978-1-4704-2393-3

Print ISSN: 0160-7642

Online ISSN: 0160-7642

Primary MSC: 20

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Publisher (non-AMS): A co-publication of the AMS and Conference Board of Mathematical Sciences

SXG Subject: AA

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Cover
- Cover
Title
- Title
Copyright
- Copyright
Contents
- Contents
Preface
- Preface
Preface to Second Printing
- Preface to Second Printing
Chapter I. Reductions to Local Subgroups and Sections
- Chapter I. Reductions to Local Subgroups and Sections
Index
- Index

Factorizations in Local Subgroups of Finite Groups

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Table of Contents

Factorizations in Local Subgroups of Finite Groups

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Cover

Title

Copyright

Contents

Preface

Preface to Second Printing

Chapter I. Reductions to Local Subgroups and Sections

Index