Product decompositions of quasirandom groups and a Jordan type theorem

Journal of the European Mathematical Society

Volumn 13, Issue 4, 2011, Pages 1063-1077

  Nikolov, N ^a   Pyber, L ^b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79956129858     PISSN: 14359855     EISSN: None     Source Type: Journal    
DOI: 10.4171/JEMS/275     Document Type: Article

References (33)

1. Aschbacher, M.: Finite Group Theory. Cambridge Univ. Press (1986) Zbl 0583.20001 MR 0895134
2. Babai, L.: On the diameter of Eulerian orientations of a graph. In: Proc. 17th Ann. Sympos. Discrete Algorithms (SODA'06), ACM-SIAM, 822-831 (2006) Zbl 1192.05084 MR 2368881
3. Babai, L., Sós, V. T.: Sidon sets in groups and induced subgraphs of Cayley graphs. Eur. J. Combin. 6, 101-114 (1985) Zbl 0573.05032 MR 0810691
4. Collins, M.: On Jordan's theorem for complex linear groups. J. Group Theory 10, 411-423 (2007) Zbl 1125.20033 MR 2334748
5. Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A., Wilson, R. A.: An Atlas of Finite Groups. Oxford Univ. Press (1985) Zbl 0568.20001 MR 0827219
6. Dixon, J. D.: The Structure of Linear Groups. Van Nostrand-Reinhold, Princeton (1971) Zbl 0232.20079 MR 0347959
7. Dornhoff, L.: Group Representation Theory. Part A: Ordinary Representation Theory. Pure Appl. Math. 7, Dekker, New York (1971) Zbl 0227.20002
8. Easdown, D., Praeger, C. E.: On minimal faithful permutation representations of finite groups. Bull. Austral. Math. Soc. 38, 207-220 (1988) Zbl 0661.20012 MR 0969911
9. Fulman, J., Guralnick, R. M.: Derangements in simple and primitive groups. In: Groups, Combinatorics and Geometry (Durham 2001), World Sci., 99-121 (2003) Zbl 1036.20002 MR 1994962
10. Gorenstein, D.: Finite Groups. Harper and Row, New York (1968) Zbl 0185.05701 MR 0231903
11. Gowers, W. T.: Quasirandom groups. Combin. Probab. Comput. 17, 363-387 (2008) Zbl 1191.20016 MR 2410393 (Pubitemid 351547539)
12. Green, B., Ruzsa, I. Z.: Sum-free sets in abelian groups. Israel J. Math. 147, 157-188 (2005) Zbl 1158.11311 MR 2166359 (Pubitemid 41411677)
13. Griess, R. L., Jr.: Automorphisms of extra special groups and nonvanishing degree 2 cohomology. Pacific J. Math. 48, 403-422 (1973) Zbl 0283.20028 MR 0476878
14. Guralnick, R. M., Lorenz, M.: Orders of finite groups of matrices. In: Groups, Rings and Algebras, Contemp. Math. 420, Amer. Math. Soc., Providence, RI, 141-161 (2006) Zbl 1203.20042 MR 2279238
15. Guralnick, R. M., Lübeck, F.: On p-singular elements in Chevalley groups in characteristic p. In: Groups and Computation. III (Columbus, OH, 1999), Ohio State Univ. Math. Res. Inst. Publ. 8, de Gruyter, Berlin, 169-182 (2001) Zbl 1001.20045 MR 1829478
16. 2 (ℤ/pℤ). Ann. of Math. 167, 601-623 (2008) Zbl pre05578700 MR 2415382
17. 3 (ℤ/pℤ). J. Eur. Math. Soc. 13, 761-851 (2011) Zbl pre05873844
18. Holt, D. F., Plesken, W.: Perfect Groups. Oxford Univ. Press (1989) Zbl 0691.20001 MR 1025760
19. Hughes, N. J. S.: The structure and order of the group of central automorphisms of a finite group. Proc. London Math. Soc. 52, 377-385 (1951) Zbl 0042.02301 MR 0041129
20. Kedlaya, K. S.: Product-free subsets of groups. Amer. Math. Monthly 105, 900-906 (1998) Zbl 0986.20025 MR 1656927 (Pubitemid 128376121)
21. Kleidman, P. B., Liebeck, M. W.: The Subgroup Structure of the Finite Classical Groups. London Math. Soc. Lecture Note Ser. 129, Cambridge Univ. Press (1990) Zbl 0697.20004 MR 1057341
22. Landazuri, V., Seitz, G. M.: On the minimal degrees of projective representations of the finite Chevalley groups. J. Algebra 32, 418-443 (1974) Zbl 0325.20008 MR 0360852
23. Larsen, M.: Word maps have large image. Israel J. Math. 139, 149-156 (2004) Zbl 1130.20310 MR 2041227 (Pubitemid 38426279)
24. Larsen, M., Shalev, A.: Word maps and Waring type problems. J. Amer. Math. Soc. 22, 437-466 (2009) Zbl 1206.20014 MR 2476780
25. Liebeck, M. W., Shalev, A.: Fuchsian groups, finite simple groups, and representation varieties. Invent. Math. 159, 317-367 (2005) Zbl 1134.20059 MR 2116277 (Pubitemid 40166696)
26. Liebeck, M. W., Shalev, A.: Simple groups, probabilistic methods, and a conjecture of Kantor and Lubotzky. J. Algebra 184, 31-57 (1996) Zbl 0870.20014 MR 1402569 (Pubitemid 126165636)
27. Lübeck, F.: Smallest degrees of representations of exceptional groups of Lie type, Comm. Algebra 29, 2147-2169 (2001) Zbl 1004.20003 MR 1837968 (Pubitemid 33392076)
28. Lucchini, A., Menegazzo, F., Morigi, M.: On the number of generators and composition length of finite linear groups. J. Algebra 243, 427-447 (2001) Zbl 0992.20033 MR 1850640 (Pubitemid 33082772)
29. Shalev, A.: Word maps, conjugacy classes, and a non-commutative Waring-type theorem. Ann. of Math. 170, 1383-1416 (2009) Zbl 1203.20013 MR 2600876
30. Shalev, A.: Mixing and generation in simple groups. J. Algebra 319, 3075-3086 (2008) Zbl 1146.20057 MR 2397424
31. Street, A. P.: Sum-free sets. In: Lecture Notes in Math. 292, Springer, 123-272 (1972) MR 0392580
32. Suprunenko, D. A.: Matrix Groups. Amer. Math. Soc., Providence (1976) Zbl 0317.20028 MR 0390025
33. Wilson, R. A.: Finite Simple Groups. Book in preparation