\(m\)th-root subgeometry partitions
It is shown that for suitable conditions on \(m\), \(n\) and \(q\), two construction methods for flag-transitive designs due to \textit{W. M. Kantor} [in: Jungnickel D., Vanstone S.A., Arasu K.T., Aschbacher M., Foote R. (eds.). Proceedings of Marshall Hall Conference (Burlington, VT, 1990), Wiley, New York 13--30 (1993)] give rise to partitions of finite projective spaces \(PG(n-1, q^m)\) into subgeometries isomorphic to \(PG(n-1, q)\) such that these subgeometries form an orbit of a cyclic collineation group. Moreover, if \(l\) divides \(m\), then every partition of \(PG(n-1, q^m)\) into subgeometries isomorphic to \(PG(n-1, q)\) gives rise to such a partition of \(PG(mn/l -1, q^l)\).
scientific article; zbMATH DE number 5536699
scientific article