3-transposition groups

Author(s)

• Aschbacher, Michael

Bibliographic Information

3-transposition groups

Michael Aschbacher

（Cambridge tracts in mathematics, 124）

Cambridge University Press, 1997

• : hardback

Other Title

Three-transposition groups

Note

Includes bibliographical references and index

Description and Table of Contents

Description

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of 3-transposition groups has become an important part of finite simple group theory, but Fischer's work has remained unpublished. 3-Transposition Groups contains the first published proof of Fischer's Theorem, written out completely in one place.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.

Table of Contents

• 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.

by "Nielsen BookData"

Details

• NCID: BA29512223
• ISBN:
  • 0521571960
• LCCN: 96026497
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: New York
• Pages/Volumes: vii, 260 p.
• Size: 24 cm
• Classification:
  • NDC9 : 411.63
  • NDC8 : 411.63
  • LCC : QA177
  • DC20 : 512/.2
• Subject Headings:
  • LCSH : Finite groups
• Parent Bibliography ID:
  • BA00134372