Products of Sylow groups
The authors prove that a finite group \(G\) is solvable if and only if the product in any order of any representative set of Sylow subgroups of \(G\) equals \(G\), where a representative set of Sylow subgroups is one that contains exactly one Sylow \(p\)-subgroup for each prime \(p\) dividing the order of the group. That confirms a conjecture made (implicitly) by Philip Hall.
scientific article; zbMATH DE number 687020