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3-transposition groups

Aschbacher, Michael, (1944-)

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3-transposition groups

Record Type:	Electronic resources : Monograph/item
Title/Author:	3-transposition groups/ Michael Aschbacher.
Author:	Aschbacher, Michael,
Published:	Cambridge :Cambridge University Press, : 1997.,
Description:	vii, 260 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
[NT 15003449]:	pt. I. Fischer's Theory. 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 -- pt. II. The existence and uniqueness of the Fischer groups. 7. Some group extensions. 8. Almost 3-transposition groups. 9. Uniqueness systems and coverings of graphs. 10. U[subscript 4](3) as a subgroup of U[subscript 6](2). 11. The existence and uniqueness of the Fischer groups -- pt. 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. Normalizers of subgroups of prime order in Fischer groups.
Subject:	Finite groups. -
Online resource:	https://doi.org/10.1017/CBO9780511759413
ISBN:	9780511759413

3-transposition groups
Aschbacher, Michael,1944-

3-transposition groups[electronic resource] /Michael Aschbacher. - Cambridge :Cambridge University Press,1997. - vii, 260 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;124. - Cambridge tracts in mathematics ;124..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

pt. I. Fischer's Theory. 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 -- pt. II. The existence and uniqueness of the Fischer groups. 7. Some group extensions. 8. Almost 3-transposition groups. 9. Uniqueness systems and coverings of graphs. 10. U[subscript 4](3) as a subgroup of U[subscript 6](2). 11. The existence and uniqueness of the Fischer groups -- pt. 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. Normalizers of subgroups of prime order in Fischer groups.

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.

ISBN: 9780511759413Subjects--Topical Terms:

532025
Finite groups.

LC Class. No.: QA177 / .A79 1997

Dewey Class. No.: 512.2

3-transposition groups
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245 1 0 $a 3-transposition groups $h [electronic resource] / $c Michael Aschbacher.
260 $a Cambridge : $b Cambridge University Press, $c 1997.
300 $a vii, 260 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge tracts in mathematics ; $v 124
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a pt. I. Fischer's Theory. 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 -- pt. II. The existence and uniqueness of the Fischer groups. 7. Some group extensions. 8. Almost 3-transposition groups. 9. Uniqueness systems and coverings of graphs. 10. U[subscript 4](3) as a subgroup of U[subscript 6](2). 11. The existence and uniqueness of the Fischer groups -- pt. 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. Normalizers of subgroups of prime order in Fischer groups.
520 $a 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.
650 0 $a Finite groups. $3 532025
830 0 $a Cambridge tracts in mathematics ; $v 124. $3 3470562
856 4 0 $u https://doi.org/10.1017/CBO9780511759413