Note on Direct Products of Certain Classes of Finite Groups

Direct products of solvable groups in which Sylow-permutability is a transitive relation are analyzed. Such groups are called 𝒫𝒮𝒯 groups, and it is well known that if the orders of two 𝒫𝒮𝒯 groups are relatively prime, then their direct product is again a 𝒫𝒮𝒯 group. Examples suggest that for solvable groups it is not necessary to have relatively prime orders to stay in the class. Some characterizations are provided, and also direct products of some other classes are discussed.