On the flocks of Q+(3,q)

Abstract

A complete characterization of the flocks of Q + (3, q) is given. As an application, it follows that if q is odd, q # 11, 23, 59, there exist no maximal exterior sets of Q + (2n -1, q) for n>2.

Maximal Baer groups in translation planes and compatibility with homology groups

“…RESULT V (Thas [42,43], Bader and Lunardon [3]). Let SF denote the set offlocks of a hyperbolic quadric in PG(3, q) and 7r F the set of corresponding translation planes (see IV).…”

“…LEMMA (3). If the order q2 > 25 then we may assume that [N1 fq N2[ = 0, 1 or q + 1 for all nets Ni of Tr which contain Baer groups of order q -1.…”

“…However, there are counterexamples when q --3, 4 or 5 and these are explicated in the article. Actually, in Section 5, we construct some new examples of maximal partial hyperbolic flocks in PG (3,5) with four conics.…”

Classification of flocks of the quadratic cone over fields of order at most 29

“…This mistake inspired Thas (1973) [39] who provided a proof for characteristic 2, and then W. F. Orr (1973) [28] provided a proof for odd characteristic in his thesis, published in [29]. Thas went on to consider flocks of Miquelian Minkowski planes, classifying them in Thas (1975) [40] for characteristic 2 and Thas (1990) [42] for fields of order Imod4, with Bader-Lunardon (1989) [1] completing the proof for fields of order 3 mod 4. Bonisoli-Korchmaros (1992) [6] provided a different proof and their introduction was understandably optimistic about the remaining Miquelian Laguerre plane case.…”

Spreads admitting net generating regulizations

“…[12, p. 3]. In [1] a complete classification of the flocks of the hyperbolic quadric of PG(3, q) is given. In PG(3, q) there exist non-regular spreads with parabolic regulization, if q is odd and q > 3; cf.…”