Subplanes of a tactical decomposition and Singer groups of a projective plane (Q1345129)

Let \(S\) be a regular collineation group of a finite projective plane \(\Pi\) and let \(M(S)\) denote the multiplier group of \(S\), i.e. the group of the automorphisms of \(S\) which induce collineations of \(\Pi\). The author investigates the structure of the 3-Sylow groups of \(M(S)\) and derives conditions which imply that \(M(S)\) is cyclic. Furthermore, he studies subgroups of \(S\) whose orbits are subplanes of \(\Pi\).