The classification of spreads in \(\text{PG}(3,q)\) admitting linear groups of order \(q(q+1)\). I: Odd order (Q1775238)

In the article are studied the spreads in \(\text{PG}(3, q)\), \(q= p^r\), \(p\) odd, whose associated planes admit linear collineation groups of order \(q(q+ 1)\), such that a Sylow \(p\)-subgroup fixes a line and acts non-trivially on it. The classification based on construction procedures is given of all such spreads.