Transitive subgroups of primitive permutation groups

Journal of Algebra

Volumn 234, Issue 2, 2000, Pages 291-361

  Liebeck, Martin W ^a   Praeger, Cheryl E ^b   Saxl, Jan ^c  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^c DPMMS   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034670402     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1006/jabr.2000.8547     Document Type: Article

References (42)

1. Aschbacher M. On the maximal subgroups of the finite classical groups. Invent. Math. 76:1984;469-514.
2. Baddeley R. W. Images of commutator maps. Comm. Algebra. 22:1994;3023-3035.
3. Baddeley R. W., Praeger C. E. On classifying all full factorisations and multiple-factorisations of the finite almost simple groups. J. Algebra. 204:1998;129-187.
4. B. Baumeister, Dual Extended Grids and a Characterisation of the Third Group of Janko, Ph.D. thesis, FU-Berlin, 1996.
5. Baumeister B. Factorizations of primitive permutation groups. J. Algebra. 194:1997;631-653.
6. Cameron P. J. Finite permutation groups and finite simple groups. Bull. London Math. Soc. 13:1981;1-22.
7. Conway J. H., Curtis R. T., Norton S. P., Parker R. A., Wilson R. A. Atlas of Finite Groups. 1985;Oxford Univ. Press, London.
8. n). J. Algebra. 70:1981;23-36.
9. Carter R. W. Conjugacy classes in the Weyl group. Borel A. Seminar on Algebraic Groups and Related Finite Groups. Springer Lecture Notes. 131:1970;Springer-Verlag, Berlin.
10. Schönert M. GAP - Groups, Algorithms and Programming. Lehrstuhl D für Mathematik. 1995;RWTH, Aachen.
11. Guralnick R., Penttila T., Praeger C. E., Saxl J. Linear groups with orders having certain large prime divisors. Proc. London Math. Soc. 78:1999;167-214.
12. Hardy G. H., Wright E. M. An Introduction to the Theory of Numbers. 1962;Oxford Univ. Press, London.
13. Hegedüs P. Regular subgroups of the affine group. J. Algebra. 225:2000;740-742.
14. Hering C. Transitive linear groups and linear groups which contain irreducible subgroups of prime order II. J. Algebra. 93:1985;151-164.
15. Hering C., Liebeck M. W., Saxl J. The factorizations of the finite exceptional groups of Lie type. J. Algebra. 106:1987;517-527.
16. Kantor W. M. k-homogeneous groups. Math. Zeit. 124:1972;261-265.
17. Kleidman P. B., Liebeck M. W. The subgroup structure of the finite classical groups. London Math. Soc. Lecture Note Series. 129:1990;Cambridge Univ. Press, Cambridge.
18. 8(q) and of their automorphism groups. J. Algebra. 110:1987;173-242.
19. 2(q), and of their automorphism groups. J. Algebra. 117:1988;30-71.
20. 4(q) and of their automorphism groups. J. Algebra. 115:1988;182-199.
21. P. B. Kleidman, The Subgroup Structure of Some Finite Simple Groups, Ph.D. thesis, University of Cambridge, 1987.
22. 22. Math. Proc. Cambridge Philos. Soc. 102:1987;17-23.
23. 4. Proc. London Math. Soc. 56:1988;484-510.
24. 23. J. London Math. Soc. 39:1989;89-101.
25. Kovacs L. G., Praeger C. E. On minimal faithful permutation representations of finite groups. Bull. Austral. Math. Soc. 62:2000;311-317.
26. Liebeck M. W. On the orders of maximal subgroups of the finite classical groups. Proc. London Math. Soc. 50:1985;426-446.
27. Liebeck M. W. The affine permutation groups of rank three. Proc. London Math. Soc. 54:1987;477-516.
28. Liebeck M. W., Praeger C. E., Saxl J. On the O'Nan-Scott theorem for finite primitive permutation groups. J. Austral. Math. Soc. 44:1988;389-396.
29. Liebeck M. W., Praeger C. E., Saxl J. The maximal factorisations of the finite simple groups and their automorphism groups. Mem. Amer. Math. Soc. 86:1990.
30. Liebeck M. W., Praeger C. E., Saxl J. A classification of the maximal subgroups of the finite alternating and symmetric groups. J. Algebra. 111:1987;365-383.
31. Liebeck M. W., Praeger C. E., Saxl J. On factorizations of almost simple groups. J. Algebra. 185:1996;409-419.
32. Liebeck M. W., Saxl J., Seitz G. M. Subgroups of maximal rank in exceptional groups of Lie type. Proc. London Math. Soc. 65:1992;297-325.
33. Liebeck M. W., Saxl J., Testerman D. M. Simple subgroups of large rank in groups of Lie type. Proc. London Math. Soc. 72:1996;425-457.
34. Liebeck M. W., Seitz G. M. Maximal subgroups of exceptional groups of Lie type, finite and algebraic. Geom. Dedicata. 36:1990;353-387.
35. Liebeck M. W., Seitz G. M. On finite subgroups of exceptional algebraic groups. J. Reine Angew. Math. 515:1999;25-72.
36. Linton S. The maximal subgroups of the Thompson group. J. London Math. Soc. 39:1989;79-88.
37. 2). J. Algebra. 139:1991;52-69.
38. Niemeyer A. C., Praeger C. E. A recognition algorithm for classical groups over finite fields. Proc. London Math. Soc. 77:1998;117-169.
39. Praeger C. E. The inclusion problem for finite primitive permutation groups. Proc. London Math. Soc. 60:1990;68-88.
40. Suzuki M. On a class of doubly transitive groups. Ann. Math. 75:1962;105-145.
41. Wielandt H. Finite Permutation Groups. 1964;Academic Press, San Diego.
42. Zsigmondy K. Zur Theorie der Potenzereste. Monatsh. Math. Phys. 3:1892;265-284.