On multiplier groups of finite cyclic planes
Let \(S\) be a cyclic group of collineations acting (sharply) transitively on the points of a finite projective plane of order \(n\); then \(S\) is called a Singer group. The multiplier group is the quotient \(M=N/S\), where \(N\) is the normalizer of \(S\) in the collineation group. The author proves the following results: The Sylow 2-subgroup of \(M\) is cyclic. If \(| M| =3k\) with \(k\in \{3,5,2^a|\) \(a\in\mathbb{N}_0\}\), then \(n=p^k\) for some prime \(p\). If \(| \Aut(S):M| \in \{2,4\}\), then \(n\leq 4\).
scientific article; zbMATH DE number 4101977