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K. Zsigmondy (1892)
Zur Theorie der PotenzresteMonatshefte für Mathematik und Physik, 3
P. Kleidman (1988)
The 2-transitive ovoidsJournal of Algebra, 117
P. Kleidman (1988)
The maximal subgroups of the Chevalley groups G2(q) with q oddJournal of Algebra
R. Wilson, J. Conway, S. Norton (1985)
ATLAS of Finite Groups
A. Brouwer, H. Wilbrink (1990)
Ovoids and fans in the generalized quadrangle Q(4, 2)Geometriae Dedicata, 36
(1962)
Arch. Math
Nick Gill (2006)
Polar spaces and embeddings of classical groupsarXiv: Group Theory
C. Charnes, U. Dempwolff (2001)
The eight dimensional ovoids over GF(5)Math. Comput., 70
A. Wispelaere, J. Huizinga, H. Maldeghem (2005)
Ovoids and spreads of the generalized hexagon H(3)Discret. Math., 305
J. Thas (1972)
Ovoidal translation planesArchiv der Mathematik, 23
C. Jansen (1995)
An Atlas of Brauer Characters
J. Conway, J. Thackray (1987)
Atlas of finite groups : maximal subgroups and ordinary characters for simple groupsMathematics of Computation, 48
Ba, Victor Kantor, G. Lunardon (2010)
Symplectic spreads from twisted fields
(1973)
Quadratic forms over GF (2), Nederl. Akad. Wetensch. Proc. Ser. A 76=Indag
(1996)
An introduction to algebraic programming in Magma
A. Blokhuis, G. Moorhouse (1995)
Some p-Ranks Related to Orthogonal SpacesJournal of Algebraic Combinatorics, 4
E. Shult (1989)
Nonexistence of ovoids in Omega+(10, 3)J. Comb. Theory, Ser. A, 51
D. Luyckx, J. Thas (2005)
Trialities and 1-Systems of Q +(7,q)Designs, Codes and Cryptography, 35
Cafer Çaliskan (2010)
On projective planes
(1990)
Old and new results on spreads and ovoids of finite classical polar spaces, Combinatorics '90 (Gaeta
W. Kantor (1982)
Strongly regular graphs defined by spreadsIsrael Journal of Mathematics, 41
R. Dye (1977)
Partitions and their stabilizers for line complexes and quadricsAnnali di Matematica Pura ed Applicata, 114
(1997)
Finite geometries, Classics in Mathematics
A. Shen (1996)
Algorithms and Programming
J. Bamberg, Tim Penttila (2008)
Overgroups of Cyclic Sylow Subgroups of Linear GroupsCommunications in Algebra, 36
A. Cossidente, G. Korchmáros (2003)
Transitive ovoids of the Hermitian surface of PG(3, q2), q evenJ. Comb. Theory, Ser. A, 101
N. Patterson (1976)
A Four-Dimensional Kerdock Set over GF(3)J. Comb. Theory, Ser. A, 20
(1995)
Handbook of incidence geometry
J. Tits (1959)
Sur la trialité et certains groupes qui s’en déduisentPublications Mathématiques de l'Institut des Hautes Études Scientifiques, 2
J. Tits (1962)
Ovoßdes et Groupes de SuzukiArchiv der Mathematik, 13
B. Bagchi, N. Sastry (1987)
Even order inversive planes, generalized quadrangles and codesGeometriae Dedicata, 22
E. Shult (1972)
On a class of doubly transitive groupsIllinois Journal of Mathematics, 16
(1989)
J. Combin. Theory Ser. A
J. Thas (1981)
Ovoids and spreads of finite classical polar spacesGeometriae Dedicata, 10
Nicholas Hamilton, C. Quinn (2000)
m-systems of polar spaces and maximal arcs in projective planesBulletin of The Belgian Mathematical Society-simon Stevin, 7
E. Shult, J. Thas (1994)
m-Systems of Polar SpacesJ. Comb. Theory, Ser. A, 68
Athula Gunawardena (2000)
Primitive Ovoids in O+8(q)J. Comb. Theory, Ser. A, 89
S. Payne, J. Thas (2009)
Finite Generalized Quadrangles
W. Kantor (1982)
Ovoids and Translation PlanesCanadian Journal of Mathematics, 34
E. Shult, J. Thas (1995)
Constructions of Polygons From BuildingsProceedings of The London Mathematical Society, 71
D. Luyckx, J. Thas (2005)
The uniqueness of the 1-system of Q-(7, q), q evenDiscret. Math., 294
Nicholas Hamilton, R. Mathon (2001)
Existence and Non-existence ofm-systems of Polar SpacesEur. J. Comb., 22
J. Thas (1980)
Polar Spaces, Generalized Hexagons and Perfect CodesJ. Comb. Theory, Ser. A, 29
A. Cossidente, O. King (2001)
Group-Theoretic Characterizations of Classical Ovoids
P. Kleidman (1987)
The maximal subgroups of the finite 8-dimensional orthogonal groups PΩ8+(q) and of their automorphism groupsJournal of Algebra, 110
Now the lines of a 1-system cover a set of (q + 1)(q 3 + 1) points. None of the orbits above are small enough for a 1-system to exist
J. Beule (2004)
The Hermitian variety H (5 , 4) has no ovoid
U. Dempwolff (1994)
Translation planes of order 27Designs, Codes and Cryptography, 4
D. Luyckx, J. Thas (2002)
The Uniqueness of the 1-System of Q - (7, q), q OddJ. Comb. Theory, Ser. A, 98
P. Kleidman, M. Liebeck (1990)
The Subgroup Structure of the Finite Classical Groups
Current address: Department of Mathematics
B. Cooperstein (1981)
Maximal subgroups of G2(2n)Journal of Algebra, 70
B. Cooperstein (1978)
Minimal degree for a permutation representation of a classical groupIsrael Journal of Mathematics, 30
Christoph Hering (1970)
Eine nicht-desarguessche zweifach transitive affine Ebene der Ordnung 27Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 34
C. O'Keefe, J. Thas (1995)
Ovoids of the quadric Q(2n, q)Eur. J. Comb., 16
D. Luyckx (2002)
m-Systems of finiite classical polar spaces
(1993)
Sz˝ onyi, Orthogonally divergent spreads of Hermitian curves, Finite geometry and combinatorics (Deinze, 1992), London Math. Soc. Lecture Note Ser
Many of the known ovoids and spreads of finite polar spaces admit a transitive group of collineations, and in 1988, P. Kleidman classified the ovoids admitting a 2-transitive group. A. Gunawardena has recently extended this classification by determining the ovoids of the seven-dimensional hyperbolic quadric which admit a primitive group. In this paper we classify the ovoids and spreads of finite polar spaces which are stabilised by an insoluble transitive group of collineations, as a corollary of a more general classification of m -systems admitting such groups.
Forum Mathematicum – de Gruyter
Published: Mar 1, 2009
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