On One Open Question of the Theory of σ -Properties of a Finite Group

Let σ ={σ _i| i∈ I} be some partition of the set of all primes and G a finite group. A subgroup A of G is σ -permutable in G provided G is σ -full; that is, G has a Hall σ _i -subgroup for all i∈ I and A permutes with all such Hall subgroups H of G; that is, AH=HA . Answering the Question 6.4 in Skiba (Probl Phys Math Tech 42(21):89–96, 2014), we get a description of finite σ -full groups G in which σ -permutability is a transitive relation.