An error was encountered while trying to add the item to the cart. Please try again.
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
Factorizations in Local Subgroups of Finite Groups

A co-publication of the AMS and CBMS
Available Formats:
Softcover ISBN: 978-0-8218-1683-7
Product Code: CBMS/33
74 pp
List Price: $29.00 Individual Price:$23.20
Electronic ISBN: 978-1-4704-2393-3
Product Code: CBMS/33.E
74 pp
List Price: $27.00 Individual Price:$21.60
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $43.50 Click above image for expanded view Factorizations in Local Subgroups of Finite Groups A co-publication of the AMS and CBMS Available Formats:  Softcover ISBN: 978-0-8218-1683-7 Product Code: CBMS/33 74 pp  List Price:$29.00 Individual Price: $23.20  Electronic ISBN: 978-1-4704-2393-3 Product Code: CBMS/33.E 74 pp  List Price:$27.00 Individual Price: $21.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$43.50
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 331977
MSC: Primary 20;

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.

• Chapters
• Chapter I. Reductions to Local Subgroups and Sections
• Chapter II. Factorizations for $p = 2$
• Chapter III. The General Situation
• Appendix Al. Proof of Theorem A
• Appendix A2. Corrections and Additions to GL
• Appendix A3.
• Request Review Copy
Volume: 331977
MSC: Primary 20;

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.

• Chapter II. Factorizations for $p = 2$