Subplanes of order 3 in Figueroa planes
The authors consider the problem concerning non--Desarguesian planes and their subplane structures on which little is still known. In particular, they consider the case of Figueroa planes of order \(q^3\). The second author showed in [J. Geom. 99, No. 1--2, 101--106 (2010; Zbl 1231.51007)] that Fano subplanes exist in Figueroa planes of order \(q^3\), \(q\) any prime power. In this paper, the case of subplanes of order \(3\) in Figueroa planes of order \(q^3\) is considered and the following theorem is proved. Theorem. Every Figueroa plane of order \(q^3\), where \(q\) is an odd prime power, has a subplane of order \(3\).
scientific article; zbMATH DE number 6146993