A class of translation affine planes of order q2, where q is a power of a prime/>>3 is constructed. These planes have an interesting property that their collineation groups are flag transitive.

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.

The projective planes of order n with a collineation group acting 2-transitively on an arc of length v, with n > v n/2, are investigated and several new examples are provided. © 2006 Elsevier Inc. All rights reserved.

We construct some classes of divisible designs from nite translation planes of dimension two and three over GF(q), q a prime power, admitting SL(2; q) as a collineation group.

in this paper, the time-like hyperruled surfaces in the minkowski 4-space and their algebraicinvariants are worked. also some characteristic results are found about these algebraic invariants.

We show that a pointwise convergent sequence (n) n2IN of continuous collineations of a compact projective plane converges uniformly if and only if the pointwise limit of (n) n2IN has a quadrangle in its image. Moreover is then a continuous collineation. Furthermore, we derive that a homomorphism between topological projective planes is continuous if and only if it is continuous at some point.