Collineation groups of projective planes of order n
نویسندگان
چکیده
منابع مشابه
PROOF OF THE PRIME POWER CONJECTURE FOR PROJECTIVE PLANES OF ORDER n WITH ABELIAN COLLINEATION GROUPS OF ORDER n
Let G be an abelian collineation group of order n2 of a projective plane of order n. We show that n must be a prime power, and that the p-rank of G is at least b+ 1 if n = pb for an odd prime p.
متن کاملOn projective planes of order 12 with a collineation group of order 9
In this paper, we prove that if π is a projective plane of order 12 admitting a collineation group G of order 9, then G is an elementary abelian group and is not planar.
متن کاملOn collineation groups of finite planes
From the Introduction to P. Dembowski’s Finite Geometries, Springer, Berlin 1968: “ . . . An alternative approach to the study of projective planes began with a paper by BAER 1942 in which the close relationship between Desargues’ theorem and the existence of central collineations was pointed out. Baer’s notion of (p, L)–transitivity, corresponding to this relationship, proved to be extremely f...
متن کاملOn Collineation Groups of Finite Projective Spaces
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...
متن کاملProjective Planes of Order 12 Do Not Have a Four Group as a Collineation Group
We have shown in [2] that the full collineation group of any projective plane of order 12 is a (2, 3) group. It is of interest to determine the structure of this (2,3} group. As a first step in that direction, we have shown in [3] that a non-Abelian group of order 6 cannot act as a collineation group on any projective plane of order 12. As a second step, we have shown in [4] that there is no pr...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1988
ISSN: 0021-8693
DOI: 10.1016/0021-8693(88)90259-1