Theory of Finite Simple Groups II

Commentary on the Classification Problems

AvGerhard Michler

Inbunden, Engelska, 2010

Del 14 i serien New Mathematical Monographs

2 772 kr

Tillfälligt slut

Beskrivning

This is a coherent explanation for the existence of the 26 known sporadic simple groups originally arising from many unrelated contexts. The given proofs build on the close relations between general group theory, ordinary character theory, modular representation theory and algorithmic algebra described in the first volume. The author presents a new algorithm by which 25 sporadic simple groups can be constructed (the smallest Mathieu group M11 can be omitted for theoretical reasons), and demonstrates that it is not restricted to sporadic simple groups. He also describes the constructions of various groups and proves their uniqueness whenever possible. The computational existence proofs are documented in the accompanying DVD. The author also states several open problems related to the theorem asserting that there are exactly 26 groups, and R. Brauer's warning that there may be infinitely many. Some of these problems require new experiments with the author's algorithm.

Produktinformation

Utgivningsdatum:2010-02-04
Mått:159 x 234 x 40 mm
Vikt:1 198 g
Format:Inbunden
Språk:Engelska
Serie:New Mathematical Monographs
Antal sidor:746
Förlag:Cambridge University Press
ISBN:9780521764919

Utforska kategorier

Algebra inom Naturvetenskap och teknik

Mer om författaren

Gerhard Michler is an Emeritus Professor of the Institute of Experimental Mathematics at the University of Duisburg-Essen and Adjunct Professor at Cornell University.

Recensioner i media

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Innehållsförteckning

Acknowledgements; Introduction; 1. Simple groups and indecomposable subgroups of GLn(2); 2. Dickson group G2(3) and related simple groups; 3. Conway's simple group Co3; 4. Conway's simple group Co2; 5. Fischer's simple group Fi22; 6. Fischer's simple group Fi23; 7. Conway's simple group Co1; 8. Janko group J4; 9. Fischer's simple group Fi'24; 10. Tits group 2F4(2)'; 11. McLaughlin group McL; 12. Rudvalis group Ru; 13. Lyons group Ly; 14. Suzuki group Suz; 15. The O'Nan group ON; 16. Concluding remarks and open problems; Appendix: Table of contents of attached DVD; References; Index.

Mer från samma författare

Vlastimil Dlab, Peter Gabriel, Gerhard Michler - Representation Theory I. Proceedings of the Fourth International Conference on Representations of Algebras, held in Ottawa, Canada, August 16-25, 1984, Häftad

Del 1177

Representation Theory I. Proceedings of the Fourth International Conference on Representations of Algebras, held in Ottawa, Canada, August 16-25, 1984

Vlastimil Dlab, Peter Gabriel, Gerhard Michler

Häftad, 1986

391 kr

Vlastimil Dlab, Peter Gabriel, Gerhard Michler - Representation Theory II. Proceedings of the Fourth International Conference on Representations of Algebras, held in Ottawa, Canada, August 16-25, 1984, Häftad

Del 1178

Representation Theory II. Proceedings of the Fourth International Conference on Representations of Algebras, held in Ottawa, Canada, August 16-25, 1984

Vlastimil Dlab, Peter Gabriel, Gerhard Michler

Häftad, 1986

391 kr

Representation Theory I. Proceedings of the Fourth International Conference on Representations of Algebras, held in Ottawa, Canada, August 16-25, 1984

Gerhard Michler, Peter Gabriel, Vlastimil Dlab

E-bok

2006

431 kr

Representation Theory II. Proceedings of the Fourth International Conference on Representations of Algebras, held in Ottawa, Canada, August 16-25, 1984

Gerhard Michler, Peter Gabriel, Vlastimil Dlab

E-bok

2006

431 kr

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Theory of Finite Simple Groups II

Commentary on the Classification Problems

AvGerhard Michler

Inbunden, Engelska, 2010

Del 14 i serien New Mathematical Monographs

2 772 kr

Tillfälligt slut

Beskrivning

Produktinformation

Utgivningsdatum:2010-02-04
Mått:159 x 234 x 40 mm
Vikt:1 198 g
Format:Inbunden
Språk:Engelska
Serie:New Mathematical Monographs
Antal sidor:746
Förlag:Cambridge University Press
ISBN:9780521764919

Utforska kategorier

Algebra inom Naturvetenskap och teknik

Mer om författaren

Gerhard Michler is an Emeritus Professor of the Institute of Experimental Mathematics at the University of Duisburg-Essen and Adjunct Professor at Cornell University.

Recensioner i media

Select Guide Rating

Innehållsförteckning

Acknowledgements; Introduction; 1. Simple groups and indecomposable subgroups of GLn(2); 2. Dickson group G2(3) and related simple groups; 3. Conway's simple group Co3; 4. Conway's simple group Co2; 5. Fischer's simple group Fi22; 6. Fischer's simple group Fi23; 7. Conway's simple group Co1; 8. Janko group J4; 9. Fischer's simple group Fi'24; 10. Tits group 2F4(2)'; 11. McLaughlin group McL; 12. Rudvalis group Ru; 13. Lyons group Ly; 14. Suzuki group Suz; 15. The O'Nan group ON; 16. Concluding remarks and open problems; Appendix: Table of contents of attached DVD; References; Index.