On primitive overgroups of quasiprimitive permutation groups

Journal of Algebra

Volumn 263, Issue 2, 2003, Pages 294-344

  Baddeley, Robert W ^a   Praeger, Cheryl E ^b  

^a Black Dog Software   (United Kingdom)

^b UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

Permutation groups; Primitive groups; Quasiprimitive groups

Indexed keywords

EID: 0038347741     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8693(03)00113-3     Document Type: Article

References (35)

1. R.W. Baddeley, Primitive permutation groups with a regular non-abelian normal subgroup, Proc. London Math. Soc. (3) 67 (3) (1993) 547-595.
2. R.W. Baddeley, Two-arc transitive graphs and twisted wreath products, J. Algebraic Combin. 2 (3) (1993) 215-237.
3. R.W. Baddeley, C.E. Praeger, On classifying all full factorisations and multiple-factorisations of the finite almost simple groups, J. Algebra 204 (1) (1998) 129-187.
4. R.W. Baddeley, C.E. Praeger, C. Schneider, Permutation groups and Cartesian decompositions, Preprint, 2002.
5. P.J. Cameron, Finite permutation groups and finite simple groups, Bull. London Math. Soc. 13 (1) (1981) 1-22.
6. A.R. Camina, C.E. Praeger, Line-transitive, point-quasiprimitive automorphism groups of finite linear spaces are affine or almost simple, Aeq. Math. 61 (2001) 221-232.
7. J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker, R.A. Wilson, Atlas of Finite Groups, Clarendon Press, Oxford, 1985.
8. X.G. Fang, C.E. Praeger, Finite two-arc transitive graphs admitting a Ree simple group, Comm. Algebra 27 (8) (1999) 3755-3769.
9. X.G. Fang, C.E. Praeger, Finite two-arc transitive graphs admitting a Suzuki simple group, Comm. Algebra 27 (8) (1999) 3727-3754.
10. R. Guralnick, T. Penttila, C.E. Praeger, J. Saxl, Linear groups with orders having certain large prime divisors, Proc. London Math. Soc. (3) 78 (1) (1999) 167-214.
11. R.M. Gurainick, Subgroups of prime power index in a simple group, J. Algebra 81 (2) (1983) 304-311.
12. B. Hartley, Fixed points of automorphisms of certain locally finite groups and Chevalley groups, J. London Math. Soc. (2) 37 (3) (1988) 421-436.
13. A. Hassani, L.R. Nochefranca, C.E. Praeger, Two-arc transitive graphs admitting a two-dimensional projective linear group, J. Group Theory 2 (4) (1999) 335-353.
14. A.A. Ivanov, C.E. Praeger, On finite affine 2-arc transitive graphs, European J. Combin. 14 (5) (1993) 421-444. Algebraic combinatorics (Vladimir, 1991).
15. G. James, A. Kerber, The Representation Theory of the Symmetric Group, Addison-Wesley, Reading, MA, 1981. With a foreword by P.M. Cohn, with an introduction by Gilbert de B. Robinson.
16. W.M. Kantor, k-homogeneous groups, Math. Z. 124 (1972) 261-265.
17. P. Kleidman, M. Liebeck, The Subgroup Structure of the Finite Classical Groups, in: London Math. Soc. Lecture Note Ser., Vol. 129, Cambridge University Press, Cambridge, 1990.
18. W. Knapp, Subkonstituenten und Struktur der Stabilisatoruntergruppe einer einfach transitiven Permutationsgruppe, PhD thesis, Eberhard-Karls-Universtät Tübingen, Tübingen, 1971.
19. W. Knapp, On the point stabilizer in a primitive permutation group, Math. Z. 133 (1973) 137-168.
20. L.G. Kovács, Primitive subgroups of wreath products in product action, Proc. London Math. Soc. (3) 58 (2) (1989) 306-322.
21. C.H. Li, The finite vertex-primitive and vertex-biprimitive s-transitive graphs with s > 3, Trans. Amer. Math. Soc. 353 (2001) 3511-3529.
22. C.H. Li, On finite s-arc transitive graphs of odd order, J. Combin. Theory Ser. B 81 (2001) 307-317.
23. M.W. Liebeck, The affine permutation groups of rank three, Proc. London Math. Soc. (3) 54 (3) (1987) 477-516.
24. M.W. Liebeck, C.E. Praeger, J. Saxl, A classification of the maximal subgroups of the finite alternating and symmetric groups, J. Algebra 111 (2) (1987) 365-383.
25. M.W. Liebeck, C.E. Praeger, J. Saxl, On the O'Nan-Scott theorem for finite primitive permutation groups, J. Austral. Math. Soc. Ser. A 44 (3) (1988) 389-396.
26. M.W. Liebeck, C.E. Praeger, J. Saxl, The maximal factorizations of the finite simple groups and their automorphism groups, Mem. Amer. Math. Soc. 86 (432) (1990), iv+151.
27. M.W. Liebeck, C.E. Praeger, J. Saxl, On factorizations of almost simple groups, J. Algebra 185 (2) (1996) 409-419.
28. M.W. Liebeck, C.E. Praeger, J. Saxl, Transitive subgroups of primitive permutation groups, J. Algebra 234 (2000) 291-361.
29. B.H. Neumann, Twisted wreath products of groups, Arch. Math. 14 (1963) 1-6.
30. A.C. Niemeyer, C.E. Praeger, A recognition algorithm for non-generic classical groups over finite fields, J. Austral. Math. Soc. Ser. A 67 (2) (1999) 223-253.
31. C.E. Praeger, The inclusion problem for finite primitive permutation groups, Proc. London Math. Soc. (3) 60 (1) (1990) 68-88.
32. C.E. Praeger, An O'Nan-Scott theorem for finite quasiprimitive permutation groups and an application to 2-arc transitive graphs, J. London Math, Soc. (2) 47 (2) (1993) 227-239.
33. C.E. Praeger, Quotients and inclusions of finite quasiprimitive permutation groups, Preprint, 2002.
34. L.L. Scott, Representations in characteristic p, in: The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979), Amer. Math. Soc., Providence, RI, 1980, pp. 319-331.
35. K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. für Math. u. Phys. 3 (1892) 265-284.