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Product Code:  SURV/40.7 
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Hardcover ISBN:  9780821840696 
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Hardcover ISBN:  9780821840696 
Product Code:  SURV/40.7 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470443870 
Product Code:  SURV/40.7.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821840696 
eBook ISBN:  9781470443870 
Product Code:  SURV/40.7.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 40; 2018; 344 ppMSC: Primary 20;
The classification of finite simple groups is a landmark result of modern mathematics. The multipart series of monographs which is being published by the AMS (Volume 40.1–40.7 and future volumes) represents the culmination of a centurylong project involving the efforts of scores of mathematicians published in hundreds of journal articles, books, and doctoral theses, totaling an estimated 15,000 pages. This part 7 of the series is the middle of a trilogy (Volume 40.5, Volume 40.7, and forthcoming Volume 40.8) treating the Generic Case, i.e., the identification of the alternating groups of degree at least 13 and most of the finite simple groups of Lie type and Lie rank at least 4. Moreover, Volumes 40.4–40.8 of this series will provide a complete treatment of the simple groups of odd type, i.e., the alternating groups (with two exceptions) and the groups of Lie type defined over a finite field of odd order, as well as some of the sporadic simple groups. In particular, this volume completes the construction, begun in Volume 40.5, of a collection of neighboring centralizers of a particularly nice form. All of this is then applied to complete the identification of the alternating groups of degree at least 13.
The book is suitable for graduate students and researchers interested in the theory of finite groups.
ReadershipGraduate students and researchers interested in the theory of finite groups.

Table of Contents

Chapters

The stages of theorem $\mathscr {C}^*_7$

General grouptheoretic lemmas

Theorem $\mathscr {C}^*_7$: Stage 3b

Theorem $\mathscr {C}^*_7$, stage 4a: Constructing a large alternating subgroup $G_0$

Properties of $\mathscr {K}$groups


Additional Material

Reviews

The presentation is just perfect. It is a tough business to present a proof which runs over three volumes. The authors take the reader by the hand, tell her or him what they are doing, and why and how it fits into the general picture. Thus, even if you are not willing to follow all the details, it gives you a good picture what the authors are doing and why this eventually yields a proof of the socalled generic case.
Gernot Stroth, Mathematical Reviews


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The classification of finite simple groups is a landmark result of modern mathematics. The multipart series of monographs which is being published by the AMS (Volume 40.1–40.7 and future volumes) represents the culmination of a centurylong project involving the efforts of scores of mathematicians published in hundreds of journal articles, books, and doctoral theses, totaling an estimated 15,000 pages. This part 7 of the series is the middle of a trilogy (Volume 40.5, Volume 40.7, and forthcoming Volume 40.8) treating the Generic Case, i.e., the identification of the alternating groups of degree at least 13 and most of the finite simple groups of Lie type and Lie rank at least 4. Moreover, Volumes 40.4–40.8 of this series will provide a complete treatment of the simple groups of odd type, i.e., the alternating groups (with two exceptions) and the groups of Lie type defined over a finite field of odd order, as well as some of the sporadic simple groups. In particular, this volume completes the construction, begun in Volume 40.5, of a collection of neighboring centralizers of a particularly nice form. All of this is then applied to complete the identification of the alternating groups of degree at least 13.
The book is suitable for graduate students and researchers interested in the theory of finite groups.
Graduate students and researchers interested in the theory of finite groups.

Chapters

The stages of theorem $\mathscr {C}^*_7$

General grouptheoretic lemmas

Theorem $\mathscr {C}^*_7$: Stage 3b

Theorem $\mathscr {C}^*_7$, stage 4a: Constructing a large alternating subgroup $G_0$

Properties of $\mathscr {K}$groups

The presentation is just perfect. It is a tough business to present a proof which runs over three volumes. The authors take the reader by the hand, tell her or him what they are doing, and why and how it fits into the general picture. Thus, even if you are not willing to follow all the details, it gives you a good picture what the authors are doing and why this eventually yields a proof of the socalled generic case.
Gernot Stroth, Mathematical Reviews