Buch, Englisch, Band 124, 270 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 446 g
Buch, Englisch, Band 124, 270 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 446 g
Reihe: Cambridge Tracts in Mathematics
ISBN: 978-0-521-10102-8
Verlag: Cambridge University Press
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of 3-transposition groups has become an important part of finite simple group theory, but Fischer's work has remained unpublished. 3-Transposition Groups contains the first published proof of Fischer's Theorem, written out completely in one place.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.
Autoren/Hrsg.
Weitere Infos & Material
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.
