On m-regular systems on \Bbb H(5, q 2)
Antonio Cossidente1
and Tim Penttila2
1Università degli Studi della Basilicata Dipartimento di Matematica e Informatica Contrada Macchia Romana 85100 Potenza Italy
2Colorado State University Department of Mathematics Fort Collins CO 80523-1874 USA
2Colorado State University Department of Mathematics Fort Collins CO 80523-1874 USA
DOI: 10.1007/s10801-008-0143-2
Abstract
The notion of m-regular system on the Hermitian variety \Bbb H( n, q 2) was introduced by B. Segre (Ann. Math. Pura Appl. 70:1-201, 1965). Here, three infinite families of hemisystems on \Bbb H(5, q 2), q odd, are constructed.
Pages: 437–445
Keywords: keywords Hermitian variety; commuting polarities; regular system; hemisystem
Full Text: PDF
References
1. Bruen, A.A., Hirschfeld, J.W.P.: Applications of line geometry over finite fields, II. The Hermitian surface. Geom. Dedicata 7(3), 333-353 (1978)
2. Cameron, P.J.: Partial quadrangles. Quart. J. Math. Oxford Ser. 26(2), 61-73 (1975)
3. Cameron, P.J., Goethals, J.M., Seidel, J.J.: Strongly regular graphs having strongly regular subconstituents. J. Algebra 55(2), 257-280 (1978)
4. Cossidente, A., King, O.H.: Maximal orthogonal subgroups of finite unitary groups. J. Group Theory 7, 447-462 (2004)
5. Cossidente, A., Penttila, T.: Hemisystems on the Hermitian surface. J. London Math. Soc. (2) 72(3), 731-741 (2005)
6. Cossidente, A., Penttila, T.: Segre's hemisystem and McLaughlin's graph. J. Comb. Theory Ser. A 115(4), 686-692 (2008)
7. Cannon, J., Playoust, C.: An introduction to MAGMA. University of Sidney, Sidney, Australia (1993)
8. Hirschfeld, J.W.P., Thas, J.A.: General Galois Geometries. Clarendon Press, Oxford (1991)
9. Kleidman, P.B.: The subgroup structure of some finite simple groups. Ph.D. Thesis, University of Cambridge (1987)
10. Kleidman, P., Liebeck, M.: The Subgroup Structure of the Finite Classical Groups. Cambridge University Press, Cambridge (1990)
11. Segre, B.: Forme e geometrie Hermitiane con particolare riguardo al caso finito. Ann. Mat. Pura Appl.
2. Cameron, P.J.: Partial quadrangles. Quart. J. Math. Oxford Ser. 26(2), 61-73 (1975)
3. Cameron, P.J., Goethals, J.M., Seidel, J.J.: Strongly regular graphs having strongly regular subconstituents. J. Algebra 55(2), 257-280 (1978)
4. Cossidente, A., King, O.H.: Maximal orthogonal subgroups of finite unitary groups. J. Group Theory 7, 447-462 (2004)
5. Cossidente, A., Penttila, T.: Hemisystems on the Hermitian surface. J. London Math. Soc. (2) 72(3), 731-741 (2005)
6. Cossidente, A., Penttila, T.: Segre's hemisystem and McLaughlin's graph. J. Comb. Theory Ser. A 115(4), 686-692 (2008)
7. Cannon, J., Playoust, C.: An introduction to MAGMA. University of Sidney, Sidney, Australia (1993)
8. Hirschfeld, J.W.P., Thas, J.A.: General Galois Geometries. Clarendon Press, Oxford (1991)
9. Kleidman, P.B.: The subgroup structure of some finite simple groups. Ph.D. Thesis, University of Cambridge (1987)
10. Kleidman, P., Liebeck, M.: The Subgroup Structure of the Finite Classical Groups. Cambridge University Press, Cambridge (1990)
11. Segre, B.: Forme e geometrie Hermitiane con particolare riguardo al caso finito. Ann. Mat. Pura Appl.