Collineation groups preserving a unital of a projective plane of odd order
نویسندگان
چکیده
منابع مشابه
Collineation Groups Preserving a Unital in a Projective Plane of Order
A unital embedded in a finite projective plane Π of order m# is a substructure of Π which forms a 2®(m$1,m1, 1) design. Several authors devoted their attention to the embedded unitals. The main aim is either to construct and investigate new classes of unitals, or to characterize some classes using group-theoretical or graphical properties [3, 6, 9, 18, 25]. In [3] we give some general results...
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It is shown that a projective plane of odd order, with a collineation group acting primitively on the points of an invariant oval, must be desarguesian. Moreover, the group is actually doubly transitive, with only one exception. The main tool in the proof is that a collineation group leaving invariant an oval in a projective plane of odd order has 2-rank at most three.
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Let V be a vector space of finite dimension n over a finite field GF(q). Let Lk(V ) denote the set of k-dimensional subspaces of V. Several authors have studied groups acting on Lk(V ) for various k. Wagner [9] considered groups which act doubly transitively on LI(V ). Recently Kantor [6] has shown that most groups which act transitively on L2(V) also act doubly transitively on LI(V ). This pap...
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The generalised projectivities (GP's) associated with projective planes of odd order are investigated. These are non-singular linear mappings over GF(2) defined from the binary codes of these planes. One case that is investigated in detail corresponds to the group of an affine plane-every point corresponds to a GP. It is shown how many collineations that fix the line at infinity point-wise can ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1989
ISSN: 0021-8693
DOI: 10.1016/0021-8693(89)90243-3