Linear groups with orders having certain large prime divisors

Proceedings of the London Mathematical Society

Volumn 78, Issue 1, 1999, Pages 167-214

  Guralnick, Robert ^a   Penttila, Tim ^b   Praeger, Cheryl E ^b   Saxl, Jan ^c  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^b UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^c UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000494142     PISSN: 00246115     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024611599001616     Document Type: Article

References (51)

1. M. ASCHBACHER, 'On the maximal subgroups of the finite classical groups', Invent. Math. 76 (1984) 469-514.
2. D. BENSON, 'Some remarks on the decomposition numbers for the symmetric groups', The Arcata conference on representations of finite groups (ed. P. Fong), Proceedings of Symposia in Pure Mathematics 47 (American Mathematical Society, Providence, R.I., 1987), pp. 381-394.
3. f)', J. Algebra 40 (1976) 75-96.
4. J. H. CONWAY, R. T. CURTIS, S. P. NORTON, R. A. PARKER and R. A. WILSON, An atlas of finite groups (Clarendon Press, Oxford, 1985).
5. U. DEMPWOLFF, 'Linear groups with large cyclic subgroups and translation planes', Rend. Sem. Mat. Univ. Padova 77 (1987) 69-113.
6. L. E. DICKSON, Linear groups with an exposition of the Galois field theory (Teubner, Leipzig, 1901; Dover, New York, 1958).
7. L. E. DICKSON, 'Representations of the general symmetric group as linear groups in finite and infinite fields', Trans. Amer. Math. Soc. 9 (1908) 121-148.
8. L. DORNHOFF, Group representation theory, Part B: modular representation theory (Marcel Dekker, New York, 1972).
9. M. GECK, 'Irreducible Brauer characters of the 3-dimensional special unitary groups in nondefining characteristic', Comm. Algebra 18 (1990) 563-584.
10. R. M. GURALNICK and W. M. KANTOR, 'Probabilistic generation of finite simple groups', preprint, University of Southern California, Los Angeles, 1997.
11. R. M. GURALNICK, K. MAGAARD and J. SAXL, 'Small cross characteristic representations for odd characteristic symplectic groups', in preparation, University of Southern California, Los Angeles, 1998.
12. R. M. GURALNICK and J. SAXL, 'Generation of finite almost simple groups by conjugates', preprint, University of Southern California, Los Angeles, 1998.
13. R. M. GURALNICK and P. H. TIEP, 'Low-dimensional representations of special linear groups in cross characteristics', Proc. London Math. Soc. (3) 78 (1999) 116-138.
14. C. HERING, 'Transitive linear groups and linear groups which contain irreducible sub-groups of prime order', Geom. Dedicata 2 (1974) 425-460.
15. C. HERING, 'Transitive linear groups and linear groups which contain irreducible subgroups of prime order, II', J. Algebra 93 (1985) 151-164.
16. G. HISS, C. JANSEN, K. LUX and R. A. PARKER, 'Computing with modular characters', preprint, University of Heidelberg, 1997.
17. G. HISS and K. LUX, Brauer trees of sporadic groups (Oxford University Press, 1989).
18. G. HISS and G. MALLE, 'Low-dimensional representations of quasi-simple groups', in preparation, University of Heidelberg, 1998.
19. I. M. ISAACS, Character theory of finite groups (Academic Press, New York, 1976; Dover, New York, 1994).
20. G. D. JAMES, 'On the minimal dimensions of irreducible representations of symmetric groups', Math. Proc. Cambridge Philos. Soc. 94 (1983) 417-424.
21. G. D. JAMES and A. KERBER, The representation theory of the symmetric group (Addison-Wesley, Reading, Mass., 1981).
22. C. JANSEN, K. LUX, R. PARKER and R. WILSON, An atlas of Brauer characters (Clarendon Press, Oxford, 1995).
23. C. JANSEN and R. A. WILSON, 'The 2-modular and 3-modular decomposition numbers for the sporadic simple O'Nan group and its triple cover', J. London Math. Soc. (2) 57 (1998) 71-90.
24. W. M. KANTOR, 'Linear groups containing a Singer cycle', J. Algebra 62 (1980) 232-234.
25. P. KLEIDMAN and M. LIEBECK, The subgroup structure of the finite classical groups, London Mathematical Society Lecture Note Series 129 (Cambridge University Press, 1990).
26. A. S. KONDRATIEV, 'Modular representations of small degree of finite groups of Lie type' (Russian), preprint, Sverdlovsk, UB. AS SSSR, 1989, 98 pp.
27. A. S. KONDRATIEV, 'Modular representations of degree ≤27 of finite quasisimple groups of alternating and sporadic types' (Russian), Trudy IMMUB RAS 1 (1992) 21-49.
28. V. LANDAZURI and G. SEITZ, 'On the minimal degrees of projective representations of the finite Chevalley groups', J. Algebra 32 (1974) 418-443.
29. M. W. LIEBECK, 'The affine permutation groups of rank three', Proc. London Math. Soc. (3) 54 (1987) 477-516.
30. M. W. LIEBECK, 'Characterization of classical groups by orbit sizes on the natural module', Proc. Amer. Math. Soc. 124 (1996) 2961-2966.
31. M. W. LIEBECK, C. E. PRAEGER and J. SAXL, The maximal factorizations of the finite simple groups and their automorphism groups, Memoirs of the American Mathematical Society 86, no. 432 (American Mathematical Society, Providence, R.I., 1990).
32. G. MALLE, J. SAXL and T. WEIGEL, 'Generation of classical groups', Geom. Dedicata 49 (1994) 85-116.
33. B. MERKT, 'Zsigmondy-Elemente in klassischen Gruppen', thesis, Tübingen, 1995.
34. B. MORTIMER, 'Groups acting on finite affine spaces', J. London Math. Soc. (2) 28 (1983) 27-30.
35. 3', Diplomarbeit, RWTH Aachen, 1991.
36. A. C. NIEMEYER and C. E. PRAEGER, 'A recognition algorithm for classical groups over finite fields', Proc. London Math. Soc. (3) 77 (1998) 117-169.
37. P. M. NEUMANN and C. E. PRAEGER, 'A recognition algorithm for special linear groups', Proc. London Math. Soc. (3) 65 (1992) 555-603.
38. I. NIVEN, H. S. ZUCKERMAN and H. L. MONTGOMERY, An introduction to the theory of numbers, 5th edn (Wiley, New York, 1991).
39. B. M. PUTTASWAMAIAH and J. D. DIXON, Modular representations of finite groups (Academic Press, New York, 1977).
40. G. SEITZ, 'Some representations of classical groups', J. London Math. Soc. (2) 10 (1975) 115-120.
41. G. M. SEITZ and A. E. ZALESSKII, 'On the minimal degrees of projective representations of the finite Chevalley groups II', J. Algebra 158 (1993) 233-243.
42. M. SCHÖNERT (ed.), Gap-3.4, manual, RWTH Aachen, 1994.
43. I. SCHUR, 'Untersuchungen über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen', J. Reine Angew. Math. 139 (1911) 155-250.
44. R. STEINBERG, Lectures on Chevalley groups, Yale University Lecture Notes, 1967.
45. P. TIEP and A. ZALESSKII, 'Minimal characters of the finite classical groups', Comm. Algebra 24 (1996) 2093-2167.
46. n over a field of characteristic 2', Math. Z. 151 (1976) 127-137.
47. n over a field of odd characteristic', Math. Z. 154 (1977) 103-114.
48. A. WAGNER, 'An observation on the degrees of projective representations of the symmetric and alternating groups over an arbitrary field', Arch. Math. 29 (1977) 583-589.
49. J. H. WALTER, 'Rigid cyclic subgroups in Chevalley groups, I', J. Algebra 131 (1990) 688-702.
50. H. WIELANDT, Finite permutation groups (Academic Press, New York, 1964).
51. K. ZSIGMONDY, 'Zur Theorie der Potenzreste', Monatsh. Für Math. u. Phys. 3 (1892) 265-284.