Finite groups acting \(2\)-transitively on their Sylow subgroups (Q1284792)

The authors completely determine: (1) all almost simple finite groups which act \(2\)-transitively on one of their sets of Sylow \(p\)-subgroups, (2) all non-abelian simple finite groups \(T\) whose automorphism group acts \(2\)-transitively on one of the sets of Sylow \(p\)-subgroups of \(T\), (3) all finite groups which are \(2\)-transitive on all their sets of Sylow subgroups. The results (1) and (3) answer the corresponding questions of \textit{B. Brewster} and \textit{M. B. Ward} [asked in Group Theory, Proc. 21st biennial Ohio State-Denison Conf. 1992, 322-325 (1993; Zbl 0829.20007)].