Sixteen-dimensional locally compact translation planes admitting SL2Has a group of collineations
نویسندگان
چکیده
منابع مشابه
Sixteen-dimensional Locally Compact Translation Planes Admitting Sl2 H as a Group of Collineations
In this paper, all 16-dimensional locally compact translation planes admitting the unimodular quaternion group SL2H as a group of collineations will be determined explicitly. Besides the classical plane over the octonions there are a vast number of planes having this property, cf. the Classification Theorem (2.8). Indeed, the class of these planes covers an interesting borderline case: Among al...
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In this paper we will give a simple construction for at least q(q + 1)/6e nondesarguesian translation planes GZ of order q6 whenever q =pe with p a prime. The elations of CY fixing the origin 0 generate a group S = SL(2, q*) having q + 2 orbits on the line L, at infinity. The group (Aut a),, has just two orbits on L,, of lengths q* + 1 and q6 q*. The kernel of LPI is GF(q3), and S acts irreduci...
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of order n on V . It follows that R induces a projective collineation φ on the (n−1)dimensional projective space PG(n−1, q). We call φ and any projective collineation conjugate to φ a Frobenius collineation. In the present paper we shall study the case n = 3, that is, the Frobenius collineations of the projective plane PG(2, q). Let P = PG(2, q). Then every Singer cycle σ (see Section 3) of P d...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2003
ISSN: 0030-8730
DOI: 10.2140/pjm.2003.209.325