Normal subgroups of SL1,D and the classification of finite simple groups

Proceedings of the Indian Academy of Sciences: Mathematical Sciences

Volumn 106, Issue 4, 1996, Pages 329-368

  Rapinchuk, Andrei ^a   Potapchik, Alexander ^b,c  

^a University of Virginia   (United States)

^b BIELEFELD UNIVERSITY   (Germany)

^c UNIVERSITY OF TORONTO   (Canada)

Author keywords

Division algebra; Finite simple group

Indexed keywords

EID: 0001742586     PISSN: 02534142     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02837693     Document Type: Article

References (24)

1. Conway J, Curtis R, Norton S, Parker R and Wilson R, Atlas of Finite Groups (Oxford: Clarendon Press) (1985)
2. Bourbaki N, Groupes et Algèbres de Lie (Hermann, Paris) (1968)
3. Bergelson V and Shapiro D, Multiplicative subgroups of finite index in a ring Proc. AMS 116(1992) 885-896
4. Feit W and Thompson J G, Solvability of groups of odd order, Pac. J. Math. 13(1963) 755-1029
5. Hall M, The Theory of Groups (New York: The Macmillan Company) (1959)
6. Kneser M, Orthogonale Gruppen über algebraicshen Zahlköpern, J. Reine Angew. Math. 196 (1956) 213-220
7. Margulis G A, Finiteness of quotient groups of discrete subgroups, Funct. Anal. i ego Prilozhenia 13 (1979) 28-39. English translation: Funct. Anal. Appl. 13(1979) 178-187
8. Margulis G A, Finiteness of quotient groups of discrete subgroups, Funct. Anal. i ego Prilozhenia 13 (1979) 28-39. English translation: Funct. Anal. Appl. 13(1979) 178-187
9. Margulis G A, On the multiplicative group of a quaternion algebra over a global field. Dokl. Akad. Nauk SSSR 252 (1980) 542-546. English translation: Sur. Math. Dokl. 21 (1980) 780-784
10. Margulis G A, On the multiplicative group of a quaternion algebra over a global field. Dokl. Akad. Nauk SSSR 252 (1980) 542-546. English translation: Sur. Math. Dokl. 21 (1980) 780-784
11. Platonov V P and Rapinchuk A S, On the group of rational points of three-dimensional groups. Dokl. Akad. Sci. USSR 247 (1979) 279-282. English translation: Sov. Math. Dokl. 20 (1979) 693-697
12. Platonov V P and Rapinchuk A S, On the group of rational points of three-dimensional groups. Dokl. Akad. Sci. USSR 247 (1979) 279-282. English translation: Sov. Math. Dokl. 20 (1979) 693-697
13. Platonov V P and Rapinchuk A S, The multiplicative structure of division algebras over number fields and the Hasse norm principle. Trudy Math. In-ta Acad. Sci. USSR 165 (1984) 171-187. English translation: Proc. Steklov Inst. Math. 165 (1985) 187-205
14. Platonov V P and Rapinchuk A S, The multiplicative structure of division algebras over number fields and the Hasse norm principle. Trudy Math. In-ta Acad. Sci. USSR 165 (1984) 171-187. English translation: Proc. Steklov Inst. Math. 165 (1985) 187-205
15. Platonov V P and Rapinchuk AS, Algebraic Groups and Number Theory (Moscow: Nauka Publishers) (1991) (English translation: Pure Appl Math. Ser. N139, Academic Press) (1993)
16. Platonov V P and Rapinchuk AS, Algebraic Groups and Number Theory (Moscow: Nauka Publishers) (1991) (English translation: Pure Appl Math. Ser. N139, Academic Press) (1993)
17. Raghunathan M S, On the group of norm 1 elements in a division algebra, Math. Ann. 279 (1988) 457-484
18. Rapinchuk A S, Benyash-Krivetz V V, Chernousov V I, Representation varieties of the fundamental groups of compact orientable surfaces. Preprint 94-030, SKB 343, Universität Bielefeld (1994)
19. Riehm C, The norm 1 group of p-adic division algebra. Am. J. Math. 92 (1970) 499-523
20. Springer T A and Steinberg R, Conjugacy classes In: Seminar on Algebraic Groups and Related Finite Groups, Lect. Notes in Math. 131 (1970) 167-266 (Berlin, Heidelberg, NY Springer)
21. Steinberg R, Lectures on Chevalley groups, Yale Univ. Lecture Notes (1967)
22. Tomanov G, On the reduced norm 1 group of a division algebra over a global field, Izv. Acad. Sci. USSR, Ser. Math. 55 (1991). English translation: Math. USSR Izvestiya 39 (1992) 895-904
23. Tomanov G, On the reduced norm 1 group of a division algebra over a global field, Izv. Acad. Sci. USSR, Ser. Math. 55 (1991). English translation: Math. USSR Izvestiya 39 (1992) 895-904
24. Turnwald G, Multiplicative subgroups of finite index in a division ring, Proc. AMS 120 (1994) 377-381