Special sets of lines in PG(3,2)
The author investigates the sets of lines in PG(3,2) having the property that every point is incident with the same number \(n\) of lines of the set and determines the orbits of these sets under PSL(4,2). In particular, numerous theorems are given about -- two disjoint spreads, -- three disjoint spreads, -- sets of \(5n\) lines, \(n\) through every point \((n = 2,3\) above all), connected with Petersen systems, -- parallelisms of spreads. The case \(n = 3\) already has been studied by \textit{F. C. Bussemarker} and \textit{J. J. Seidel} [report TU Eindhoven (1970; Zbl 0324.05015) or Ann. New York Acad. Sci. 175, 66-79 (1970; Zbl 0239.05010)]. They use a combinatorial approach. The investigations in this paper have more geometric flavor, and by case \(n = 3\) are given all possibilities.
scientific article; zbMATH DE number 803764