Finite simple groups which projectively embed in an exceptional Lie group are classified!

Bulletin of the American Mathematical Society

Volumn 36, Issue 1, 1999, Pages 75-93

  Griess Jr , Robert L ^a   Ryba, A J E ^b,c  

^a UNIVERSITY OF MICHIGAN   (United States)

^b MARQUETTE UNIVERSITY   (United States)

^c CITY UNIVERSITY OF NEW YORK   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033477994     PISSN: 02730979     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0273-0979-99-00771-5     Document Type: Article

References (88)

1. A. V. Alekseevski, Finite commutative Jordan subgroups of complex simple Lie groups, Functional Analysis Appl. 8 (1974), 277-279. MR 52:653
2. A. V. Alekseevski, Finite commutative Jordan subgroups of complex simple Lie groups, Functional Analysis Appl. 8 (1974), 277-279. MR 52:653
3. A. Borovik, On the structure of finite subgroups of the simple algebraic groups, Algebra and Logic 28 (1989), 249-279 (in Russian). MR 91h:20071
4. A. Borovik, On the structure of finite subgroups of the simple algebraic groups, Algebra and Logic 28 (1989), 249-279 (in Russian). MR 91h:20071
5. A. Borovik, Finite subgroups of simple algebraic groups, Soviet Math. Dokl. 40, 570-573, (translation). MR 90m:20051
6. A. Borovik, Finite subgroups of simple algebraic groups, Soviet Math. Dokl. 40, 570-573, (translation). MR 90m:20051
7. A. Borel and J.-P. Serre, Sur certains sous-groupes de Lie compacts, Comment. Hath. Helv., 27(1953), 128-139. MR 14:948d
8. A. Borel and J.-P. Serre, Sur certains sous-groupes de Lie compacts, Comment. Hath. Helv., 27(1953), 128-139. MR 14:948d
9. R. W. Carter, Simple Groups of Lie Type, John Wiley and Sons, London, 1989. MR 90g:20001
10. R. W. Carter, Simple Groups of Lie Type, John Wiley and Sons, London, 1989. MR 90g:20001
11. 8, Proc. Symp. Pure Math. 47 (1987), 367-405. MR 90a:20089
12. 8, Proc. Symp. Pure Math. 47 (1987), 367-405. MR 90a:20089
13. Arjeh Cohen and Robert L. Griess, Jr, Non-Local Lie primitive subgroups of Lie groups, Can. J. Math. 45 (1)(1993), 88-103. MR 94a:22012
14. Arjeh Cohen and Robert L. Griess, Jr, Non-Local Lie primitive subgroups of Lie groups, Can. J. Math. 45 (1)(1993), 88-103. MR 94a:22012
15. 8, Comm. in Algebra, 21(6), 1889-1907 (1993). MR 94m:20041
16. 8, Comm. in Algebra, 21(6), 1889-1907 (1993). MR 94m:20041
17. Arjeh M. Cohen and Gary M. Seitz, The r-rank of the groups of exceptional Lie type, Nederl. Akad. Wetensch. Indag. Math. 49 (1987), no. 3, 251-259. MR 88k:20062
18. Arjeh M. Cohen and Gary M. Seitz, The r-rank of the groups of exceptional Lie type, Nederl. Akad. Wetensch. Indag. Math. 49 (1987), no. 3, 251-259. MR 88k:20062
19. 2(ℂ), Comm. Algebra 11 (1983), 441-459. MR 85b:20010
20. 2(ℂ), Comm. Algebra 11 (1983), 441-459. MR 85b:20010
21. 6. Israel Journal of Mathematics, 82 (1993), 45-86. MR 94h:20020
22. 6. Israel Journal of Mathematics, 82 (1993), 45-86. MR 94h:20020
23. Arjeh Cohen and David Wales, Finite simple subgroups of semisimple complex Lie groups - a survey, from Groups of Lie Type and their Geometries, edited by W. M. Kantor and L. Di Martino, Cambridge University Press 1995. MR 96e:20021
24. Arjeh Cohen and David Wales, Finite simple subgroups of semisimple complex Lie groups - a survey, from Groups of Lie Type and their Geometries, edited by W. M. Kantor and L. Di Martino, Cambridge University Press 1995. MR 96e:20021
25. 6(ℂ), Proc. London Math. Soc., (3) 74 (1997), 105-150. MR 97k:20078
26. 6(ℂ), Proc. London Math. Soc., (3) 74 (1997), 105-150. MR 97k:20078
27. Coxeter, H. S. M., Integral Cayley numbers, Duke Math. J. 13 (1946), 561-578. MR 8:370b
28. Coxeter, H. S. M., Integral Cayley numbers, Duke Math. J. 13 (1946), 561-578. MR 8:370b
29. Walter Feit, Characters of Finite Groups, Benjamin, New York, 1967. MR 36:2715
30. Walter Feit, Characters of Finite Groups, Benjamin, New York, 1967. MR 36:2715
31. P. Fong and R. Griess, An infinite family of elementwise conjugate nonconjugate homomorphisms, International Mathematics Research Notices, 1995, 5, 249-252. MR 96e:20029
32. P. Fong and R. Griess, An infinite family of elementwise conjugate nonconjugate homomorphisms, International Mathematics Research Notices, 1995, 5, 249-252. MR 96e:20029
33. 8, Thesis, University of Michigan, 1995.
34. 8, Memoirs of the American Mathematical Society, to appear.
35. 6, to appear in Journal of Algebra.
36. D. Frey and R. Griess, The conjugacy classes of elements in the Borovik group, Journal of Algebra 203 (1998), 226-243. CMP 98:12
37. D. Frey and R. Griess, The conjugacy classes of elements in the Borovik group, Journal of Algebra 203 (1998), 226-243. CMP 98:12
38. G. Frobenius, Über die cogredienten Transformationen der bilinearen Formen, S.-B. Preuss. Akad. Wiss. (Berlin) 7-16 (1896); Gesammelte Abhandlungen, II , 695-704.
39. G. Frobenius, Über die cogredienten Transformationen der bilinearen Formen, S.-B. Preuss. Akad. Wiss. (Berlin) 7-16 (1896); Gesammelte Abhandlungen, II , 695-704.
40. Daniel Gorenstein, Finite Groups, Harper and Row, New York, 1968. MR 38:229
41. Daniel Gorenstein, Finite Groups, Harper and Row, New York, 1968. MR 38:229
42. Robert L. Griess, Jr., Elementary Abelian p-Subgroups of Algebraic Groups, Geom. Dedicata 39 (1991), 253-305. MR 92i:20047
43. Robert L. Griess, Jr., Elementary Abelian p-Subgroups of Algebraic Groups, Geom. Dedicata 39 (1991), 253-305. MR 92i:20047
44. 2, Invent. Math., 121 (1995) 257-277. MR 96f:20065
45. 2, Invent. Math., 121 (1995) 257-277. MR 96f:20065
46. Robert L. Griess, Jr., Twelve Sporadic Groups, Springer Mathematical Monograph, Springer Verlag, 1998.
47. 7, Inventiones Math. 116 , 215-241 (1994). MR 94k:20024
48. 7, Inventiones Math. 116 , 215-241 (1994). MR 94k:20024
49. 8(ℂ), Duke Math. Journal 94 (1998), 181-211. CMP 98:16
50. 8(ℂ), Duke Math. Journal 94 (1998), 181-211. CMP 98:16
51. 8(ℂ), to appear in Journal of Symbolic Computation.
52. Robert L. Griess, Jr. and A. J. E. Ryba, The finite quasisimple groups which embed in exceptional Lie groups. Preprint.
53. Robert L. Griess, Jr. and A. J. E. Ryba, Embeddings of Sz(8) into exceptional Lie groups. Preprint.
54. B. Huppert, Endliche Gruppen I, Springer Verlag, Berlin, 1968. MR 37:302
55. B. Huppert, Endliche Gruppen I, Springer Verlag, Berlin, 1968. MR 37:302
56. I. Martin Isaacs, Character Theory of Finite Groups, Academic Press, 1976. MR 57:417
57. I. Martin Isaacs, Character Theory of Finite Groups, Academic Press, 1976. MR 57:417
58. Zvonimir Janko, A new finite simple group with abelian Sylow 2-subgroups and its characterization, J. Algebra 3 147-186 (1966). MR 33:1359
59. Zvonimir Janko, A new finite simple group with abelian Sylow 2-subgroups and its characterization, J. Algebra 3 147-186 (1966). MR 33:1359
60. 8(ℂ) and their Actions on a Maximal Torus, Thesis, University of Michigan, 1996.
61. 7(ℂ), J. AIg. 161(2), 535-540 (1993). MR 94k:20025
62. 7(ℂ), J. AIg. 161(2), 535-540 (1993). MR 94k:20025
63. B. Kulshammer, Algebraic representations of finite groups, Universität Augsburg, 1992.
64. M. Larsen, On the conjugacy of element-conjugate homomorphisms, Israel Journal, 88 (1994), 253-277. MR 95k:20073
65. M. Larsen, On the conjugacy of element-conjugate homomorphisms, Israel Journal, 88 (1994), 253-277. MR 95k:20073
66. M. Larsen, On the conjugacy of element-conjugate homomorphisms, II, Quart. J. Math. Oxford Ser. (2) 47 (1996), 73-85. MR 97b:20070
67. M. Larsen, On the conjugacy of element-conjugate homomorphisms, II, Quart. J. Math. Oxford Ser. (2) 47 (1996), 73-85. MR 97b:20070
68. A. I. Mal'cev, Semisimple subgroups of Lie groups, Amer. Math. Soc. Translations 1, 172-273 (1962).
69. John McKay, Finite Groups - Coming of Age, Proc. Can. Math. Soc. Conf., held June 15-28, 1982, Amer. Math. Soc., Providence, RI, 1985, 271-285. MR 86j:20002
70. John McKay, Finite Groups - Coming of Age, Proc. Can. Math. Soc. Conf., held June 15-28, 1982, Amer. Math. Soc., Providence, RI, 1985, 271-285. MR 86j:20002
71. 2(q) invariant theory in the rank two Lie groups, Comm. Alg., 24 (1996), no. 6, 1915-1938. MR 97g:20020
72. 2(q) invariant theory in the rank two Lie groups, Comm. Alg., 24 (1996), no. 6, 1915-1938. MR 97g:20020
73. p) dans des groupes de Lie simples, Inventiones Math. 124, 525-562 (1996). MR 97d:20056
74. p) dans des groupes de Lie simples, Inventiones Math. 124, 525-562 (1996). MR 97d:20056
75. J-P. Serre, Personal Communication, 1998.
76. Peter Slodowy, Two notes on a finiteness problem in the representation theory of finite groups, Hamburger Beiträge zur Mathematik, aus dem Mathematischen Seminar, Heft 21; 1993. Published in "Algebraic Groups and Lie Groups" (A volume of papers in honour of the late R.W. Richardson), Ed. G.I. Lehrer, Australian Math. Soc. Lecture Series No. 9, Cambridge University Press, Cambridge, 1997; pages 331-346. CMP 98:16
77. Peter Slodowy, Two notes on a finiteness problem in the representation theory of finite groups, Hamburger Beiträge zur Mathematik, aus dem Mathematischen Seminar, Heft 21; 1993. Published in "Algebraic Groups and Lie Groups" (A volume of papers in honour of the late R.W. Richardson), Ed. G.I. Lehrer, Australian Math. Soc. Lecture Series No. 9, Cambridge University Press, Cambridge, 1997; pages 331-346. CMP 98:16
78. Peter Slodowy, Two notes on a finiteness problem in the representation theory of finite groups, Hamburger Beiträge zur Mathematik, aus dem Mathematischen Seminar, Heft 21; 1993. Published in "Algebraic Groups and Lie Groups" (A volume of papers in honour of the late R.W. Richardson), Ed. G.I. Lehrer, Australian Math. Soc. Lecture Series No. 9, Cambridge University Press, Cambridge, 1997; pages 331-346. CMP 98:16
79. T. A. Springer, Regular elements of finite reflection groups, Inventiones Math. 25 (1974), 159-198. MR 50:7371
80. T. A. Springer, Regular elements of finite reflection groups, Inventiones Math. 25 (1974), 159-198. MR 50:7371
81. Jacques Tits, Sous-algèbres des algèbres de Lie semi-simples (d'apres V. Morosov, A. Malcev, E.Dynkin et F. Karpelevitch), Séminaire Bourbaki, No. 119, May 1955. CMP 98:09
82. Jacques Tits, Sous-algèbres des algèbres de Lie semi-simples (d'apres V. Morosov, A. Malcev, E.Dynkin et F. Karpelevitch), Séminaire Bourbaki, No. 119, May 1955. CMP 98:09
83. David Wales, Finite linear groups of degree 7, Canadian J. Math. 21, 1025-1041 (1969) [see also Bull. Amer. Math. Soc. 74, 197-198 (1968). MR 40:1489
84. David Wales, Finite linear groups of degree 7, Canadian J. Math. 21, 1025-1041 (1969) [see also Bull. Amer. Math. Soc. 74, 197-198 (1968). MR 40:1489
85. David Wales, Finite linear groups of degree 7, Canadian J. Math. 21, 1025-1041 (1969) [see also Bull. Amer. Math. Soc. 74, 197-198 (1968). MR 40:1489
86. A. Weil, Remarks on the cohomology of groups, Ann. Math. 80 (1964), 149-157; also [1964a], vol.3 in Oeuvres scientifiques ; Collected papers / Andre Weil. New York : Springer-Verlag (1979), 3 volumes. MR 30:199
87. A. Weil, Remarks on the cohomology of groups, Ann. Math. 80 (1964), 149-157; also [1964a], vol.3 in Oeuvres scientifiques ; Collected papers / Andre Weil. New York : Springer-Verlag (1979), 3 volumes. MR 30:199
88. A. Weil, Remarks on the cohomology of groups, Ann. Math. 80 (1964), 149-157; also [1964a], vol.3 in Oeuvres scientifiques ; Collected papers / Andre Weil. New York : Springer-Verlag (1979), 3 volumes. MR 30:199