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Theory of Finite Simple Groups II: Commentary on the Classification Problems (New Mathematical Monographs)

Theory of Finite Simple Groups II: Commentary on the Classification Problems (New Mathematical Monographs)

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Gerhard Michler
Cambridge University Press, 2/4/2010
EAN 9780521764919, ISBN10: 0521764912

Hardcover, 746 pages, 22.8 x 15.2 x 4 cm
Language: English

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.

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.