Groups 2-Transitive on a set of their Sylow subgroups
Groups 2-Transitive on a set of their Sylow subgroups
We classify, modulo the kernel of the action, finite groups G that act 2-transitively on Syl r ( G ) for some prime r dividing | G |. We furthermore prove that any finite group that acts 2-transitively on Syl r ( G ) for each prime r is solvable …