Theory of Finite Simple Groups II

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. Brauers warning that there may be infinitely many. Some of these problems require new experiments with the authors algorithm.

Spis treści:
Acknowledgements
Introduction
1. Simple groups and indecomposable subgroups of GLn(2)
2. Dickson group G2(3) and related simple groups
3. Conways simple group Co3
4. Conways simple group Co2
5. Fischers simple group Fi22
6. Fischers simple group Fi23
7. Conways simple group Co1
8. Janko group J4
9. Fischers simple group Fi24
10. Tits group 2F4(2)
11. McLaughlin group McL
12. Rudvalis group Ru
13. Lyons group Ly
14. Suzuki group Suz
15. The ONan group ON
16. Concluding remarks and open problems
Appendix, Table of contents of attached DVD
References
Index.