The non-solvable rank 3 affine planes

Journal of Combinatorial Theory. Series A

Volumn 93, Issue 2, 2001, Pages 201-230

  Biliotti, Mauro ^a   Johnson, Norman L ^b  

^a UNIVERSITY OF SALENTO   (Italy)

^b UNIVERSITY OF IOWA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035255623     PISSN: 00973165     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcta.2000.3074     Document Type: Article

References (40)

1. Biliotti M., Jha V., Johnson N. L. The collineation groups of generalized twisted field planes. Geom. Dedicata. 76:1999;97-126.
2. Buekenhout F., Delandtsheer A., Doyen J., Kleidman P. B., Liebeck M., Saxl J. Linear spaces with flag-transitive automorphism groups. Geom. Dedicata. 36:1990;89-94.
3. Buekenhout F. Handbook of Incidence Geometry. 1995;North-Holland, Amsterdam.
4. Cordero M., Figueroa R. Transitive autotopism groups and the generalized twisted field planes. Mostly Finite Geometries, Iowa City, IA, 1996. Lecture Notes in Pure and Appl. Math. 190:1997;Dekker, New York.
5. Charnes C., Dempwolff U. The translation planes of order 49 and their automorphisms groups. Math. Comp. 67:1998;1207-1224.
6. Cooperstein B. N. Minimal degree for a permutation representation of a classical group. Israel J. Math. 30:1978;213-235.
7. Czerwinski T. The collineation groups of the translation planes of order 25. Geom. Dedicata. 39:1991;125-137.
8. Dembowski P. Finites Geometries. 1968;Springer-Verlag, Berlin/Heidelberg/New York.
9. Dixon J. D., Mortimer B. Permutation Groups. 1996;Springer-Verlag, Berlin/Heidelberg/New York.
10. Foulser D. A. Baer p-elements in translation planes. J. Algebra. 31:1974;354-366.
11. 2 that admit SL(2, q) as a collineation group. II. Odd order. J. Geom. 18:1982;122-139.
12. 2 that admit SL(2, q) as a collineation group. I. Even order. J. Algebra. 86:1984;385-406.
13. Foulser D. A., Kallaher M. J. Solvable, flag-transitive, rank 3 collineation groups. Geom. Dedicata. 7:1978;111-130.
14. M. Ganley, V. Jha, and N. L. Johnson, The translation planes admitting a nonsolvable doubly transitive line-sized orbit, J. Geom., in press.
15. n). Ann. Math. 27:1926;140-158.
16. Hering C. Transitive linear groups which contain irreducible subgroups of prime order. Geom. Dedicata. 2:1974;425-466.
17. ∞. J. Algebra. 162:1993;392-409.
18. Jagannathan T. V. S., Srinivasan P. Near-field-like planes. Finite Geometries Winnipeg, Man., 1984. Lecture Notes in Pure and Appl. Math. 103:1985;Dekker, New York.
19. Jha V., Johnson N. L. Derivable nets defined by central collineations. J. Combin. Inform. System Sci. 11:1986;83-91.
20. Jha V., Kallaher M. J. On spreads admitting projective linear groups. Canad. J. Math. 33:1981;1487-1497.
21. Johnson N. L. Representations of SL(2, 4) on translation planes of even order. J. Geom. 21:1983;184-200.
22. 2 that admit q+1 elations. Geom. Dedicata. 15:1984;329-337.
23. Kallaher M. J. On finite affine planes of rank 3. J. Algebra. 13:1969;544-553.
24. Kallaher M. J. Translation planes admitting solvable rank 3 collineation groups. Geom. Dedicata. 6:1977;305-329.
25. Kallaher M. J., Ostrom T. G. Collineation groups irreducible on the components of a translation plane. Geom. Dedicata. 9:1980;153-194.
26. Kleidman P., Liebeck M. The Subgroup Structure of the Finite Classical Groups. 1990;Cambridge Univ. Press, Cambridge.
27. Korchmaros G. A translation plane or order 49 with non-solvable collineation group. J. Geom. 24:1985;18-30.
28. Liebeck M. W. The affine permutation groups of rank three. Proc. London Math. Soc. (3). 54:1987;477-516.
29. Liebeck M. W. The classification of finite linear spaces with flag-transitive automorphism groups of affine type. J. Combin. Theory Ser. A. 84:1998;196-235.
30. Liebler R. A. Finite affine planes of rank three are translation planes. Math. Z. 116:1970;89-93.
31. Lüneburg H. Translation Planes. 1980;Springer-Verlag, Berlin/Heidelberg/New York.
32. 2 which admit SL(2, 9). Geom. Dedicata. 17:1985;297-305.
33. 2 and of extra-special type. Geom. Dedicata. 17:1985;307-322.
34. Mazurov V. D. Minimal permutation representation of finite simple classical groups. Special linear, symplectic, and unitary groups. Algebra i Logika. 32:1993;267-287.
35. Mazurov V. D., Vasil'ev V. A. Minimal permutation representation of finite simple orthogonal groups. Algebra i Logika. 33:1994;603-627.
36. Mitchell H. H. Determination of the ordinary and modular ternary linear groups. Trans. Amer. Math. Soc. 12:1911;207-242.
37. Ostrom T. G. Nets with critical deficiency. Pacific J. Math. 14:1964;1381-1387.
38. Ostrom T. G. Collineation groups whose order is prime to the characteristic. Math. Z. 156:1977;56-71.
39. Ostrom T. G. Elementary abelian 2-groups on the line at infinity of translation planes. J. Geom. 17:1981;128-139.
40. Woltermann M. A note on doubly transitive solvable permutation groups. Comm. Algebra. 7:1979;1877-1883.