JOURNAL OF
ALGEBRAIC
COMBINATORICS

Home > Vol 5, No 2 (1996)

Hans Cuypers and Antonio Pasini

We classify finite flag-transitive geometries of rank n ( A _{n - 2} . L ^* . L)        \cdot  - - \cdot  - \cdot \cdot \cdot \cdot \cdot  - \cdot  - - \cdot  - - \cdot  - - \cdot  ^{L * L} (A_{n - 2} .L^ * .L)\;\;\;\; \cdot - - \cdot - \cdot \cdot \cdot \cdot \cdot - \cdot - - \cdot - - \cdot - - \cdot ^{L^* L}

1. A. Blokhuis and A. Brouwer, "Locally 4-by-4 grid graphs," J. Graph Th. 13 (1989), 229-244.
2. F. Buekenhout, "Diagrams for geometries and groups," J. Comb. Th. (A) 27 (1979), 121-151.
3. F. Buekenhout, "Diagram geometries for sporadic groups," in Finite Groups Coming of Age, A.M.S. Series Contemp. Math. 45 (1985), 1-32.
4. F. Buekenhout, A. Delandtsheer, and J. Doyen, "Finite linear spaces with flag-transitive groups," J. Comb. Th.(A) 49 (1988), 268-293.
5. F. Buekenhout and A. Pasini, "Finite diagram geometries extending buildings," Chapter 22 of Handbook of Incidence Geometry, F. Buekenhout (Ed.), Elsevier, Amsterdam, 1995 .
6. P. Cameron, "Finite permutation groups and finite simple groups," Bull. London Math. Soc. 13(1981), 1-22.
7. J. Conway, R. Curtis, S. Norton, R. Parker, and R. Wilson, Atlas of Finite Groups, Clarendon Press, Oxford,
1985. CUYPERS AND PASINI
8. A. Cohen and H. Zantema, "A computation concerning doubly transitive permutation groups," J. Reine und Angewandte Math. 34 (1984), 196-211.
9. H. Cuypers, "On delta spaces satisfying Pasch's axiom," to appear in J. Geom.
10. H. Cuypers, "Symplectic geometries, transvection groups and modules," J. Comb. Th. (A) 65 (1994), 39-59.
11. H. Cuypers, "Affine Grassmannians," to appear in J. Comb. Th. (A).
12. A. Delandtsheer, "Dimensional linear spaces whose automorphism group is (line-hyperplane)-flag transitive," Des. Codes and Crypt. 1 (1991), 237-245.
13. A. Del Fra and D. Ghinelli, "Af*.Af-geometries, the Klein quadric and Hn " Discrete Math. 129 (1994), 53-74.
14. J. Hall, "Graphs, geometry, 3-transpositions and symplectic F2-transvection groups," Pwc. London Math. Soc. 58(1989), 89-111.
15. J. Hall, "Some 3-transposition groups with normal 2-subgroups," Proc. London Math. Soc. 58 (1989), 112- 136.
16. M. Hall and E. Shult, "Geometric hyperplanes of non-embeddable grassmannians," European J. Comb. 14 (1993), 29-36.
17. C. Hering, "Transitive linear groups and linear groups which contain irreducible subgroups of prime order," Geom. Dedicata 2 (1974), 425-460.
18. C. Hering, "Transitive linear groups and linear groups which contain irreducible subgroups of prime order, II," J. Algebra 27 (1985), 57-111.
19. D. Higman, "Flag-transitive collineation groups of finite projective spaces," Illinois J. Math. 6 (1962), 434-446.
20. D. Hughes, "Extensions of designs and groups: Projective, symplectic and certain affine groups," Math. Z. 89(1965),199-205.
21. M. Liebeck, "The affine permutation groups of rank three," Proc. London Math. Soc. (3) 54 (1987), 477-516.
22. T. Meixner and A. Pasini, "A census of known flag-transitive extended grids," in Finite Geometry and Combinatorics, L.M.S. Lecture Notes Ser. 191, F. De and Clerck et al. (Eds.), Cambridge Univ. Press, Cambridge, 1993.
23. A. Pasini, "On extended grids with large automorphism groups," Ars. Comb. 29 (1990), 643-658.
24. A. Pasini, "A bound for the collinearity graph of certain locally polar geometries," J. Comb. Th. (A) 58 (1991), 127-130.
25. A. Pasini, An Introduction to Diagram Geometry, Oxford Univ. Press, Oxford, 1994.
26. S.Rinauro, "On some extensions of generalized quadrangles of grid type,"J Geometry38(1990), 158-164.
27. E. Shult, "Geometric hyperplanes of embeddable grassmannians," J. Algebra 145 (1992), 55-82.
28. A. Sprague, "Rank 3 incidence structures admitting dual-linear, linear diagram," J. Comb. Th. (A) 38 (1985), 254-259.