3-Transposition Groups (Cambridge Tracts in Mathematics, 124, Band 124).

Aschbacher, Michael:

ISBN 10: 0521101026 / ISBN 13: 9780521101028

Published by Cambridge University Press, 2009

About this Item

272 S. Das Buch ist in sehr gutem, sauberen Zustand. Ecken und Kanten leicht bestossen. Sonst sauberes und wohlerhaltenes Exemplar. -----Inhalt:. The theory of 3-transposition groups has become an important part of finite simple group theory. This book contains the first complete published proof of Fischer's Theorem on the classification of these groups. Part I is accessible to graduate students in finite groups while Parts II and III are aimed at specialists.In 1970 Bernd Fischer proved his beautiful theorem classifying the almost simple groups generated by 3-transpositions, and in the process discovered three new sporadic groups, now known as the Fischer groups. Since then, the theory of 3-transposition groups has become an important part of finite simple group theory, but Fischer's work has remained unpublished. 3-Transposition Groups contains the first published proof of Fischer's Theorem, written out completely in one place. Fischer's result, while important and deep (covering a number of complex examples), can be understood by any student with some knowledge of elementary group theory and finite geometry. Thus Part I has minimal prerequisites and could be used as a text for an intermediate level graduate course. Parts II and III are aimed at specialists in finite groups and are a step in the author's program to supply a strong foundation for the theory of sporadic groups. Part I. Fischer's Theorem: 1. Preliminaries; 2. Commuting graphs of groups; 3. The structure of 3-transposition groups; 4. Classical groups generated by 3-transpositions; 5. Fischer's theorem; 6. The geometry of 3-transposition groups; Part II. Existence and Uniquenesss Of The Fischer Groups: 7. Some group extensions; 8. Almost 3-transposition groups; 9. Uniqueness systems and coverings of graphs; 10. U4 (3) as a subgroup of U6 (2); 11. The existence and uniqueness of the Fischer groups; Part III. The Local Structure Of The Fischer Groups: 12. The 2-local structure of the Fischer groups; 13. Elements of order 3 in orthogonal groups over GF(3); 14. Odd locals in Fischer groups; 15. Normalisers of subgroups of prime order in Fischer groups. ISBN: 9780521101028 Aufgrund neuer EU Verpackungsgesetze können wir zurzeit nicht in EU Länder außer Deutschland liefern, Lieferungen an Grenz Packstationen oder Grenzpaket Anbieter ist weiterhin möglich. Auch Lieferungen in alle Länder außer der EU und Russland sind weiterhin möglich. Due to new EU packaging regulations, we are currently unable to ship to EU countries other than Germany; however, deliveries to border-located parcel lockers or cross-border parcel services remain possible. Shipments to all countries outside the EU and Russia also remain possible. Sprache: Englisch Gewicht in Gramm: 400.

Seller Inventory # 669119

Bibliographic Details

• Title: 3-Transposition Groups (Cambridge Tracts in Mathematics, 124, Band 124).
• Publisher: Cambridge University Press
• Publication Date: 2009
• Language: English
• ISBN 10: 0521101026
• ISBN 13: 9780521101028
• Binding: Broschiert, Gr.-8°
• Edition: 1.
• Condition: Sehr gut
• Weight: 400 grams
• Seller catalogs:
  • Mathematik

About this title

Synopsis

In 1970 Bernd Fischer proved his beautiful theorem classifying the almost simple groups generated by 3-transpositions, and in the process discovered three new sporadic groups, now known as the Fischer groups. Since then, the theory of 3-transposition groups has become an important part of finite simple group theory, but Fischer's work has remained unpublished. 3-Transposition Groups contains the first published proof of Fischer's Theorem, written out completely in one place. Fischer's result, while important and deep (covering a number of complex examples), can be understood by any student with some knowledge of elementary group theory and finite geometry. Thus Part I has minimal prerequisites and could be used as a text for an intermediate level graduate course. Parts II and III are aimed at specialists in finite groups and are a step in the author's program to supply a strong foundation for the theory of sporadic groups.

Review

'Just to make available the Fischer theory to the mathematical community would justify this book. Moreover, we find a great many of interesting properties of the Fischer groups and others which are spread over the literature or may be known to specialists but cannot be found anywhere.' W. Willems, Magdeburg

' ... this book offers a profound insight into the theory of finite simple groups even for non-specialists.' G. Kowol, Monatshefte für Mathematik

'The author's main objective is to provide a proof of the theorem classifying the almost simple groups generated by 3-transpositions, which Bernd Fischer found in 1970 but never published ... A specialised but important topic, which is given a very readable exposition here.' Mathematika

'I recommend the book strongly to two types of potential reader: the reader who wishes to see a proof of a beautiful and key theorem in the classification theorem explained by a master and the reader who is already expert in finite group theory and who wishes to gain detailed insight into the current programme of placing the theory of sporadic simple groups in a conceptual framework.' Proceedings of the Edinburgh Mathematical Society

' ... its place as an important reference work is assured, and it should be in every serious finite group theorist's library.' Bull. of London Math. Soc.

'If you have any interest in group theory, then you got to have this book.' Bulletin of the Belgian Mathematical Society