A Robinson description of finite PσT-groups.

Let σ = { σ i | i ∈ I } be some partition of the set of all primes P and G a finite group. Then G is said to be σ-full if G has a Hall σ i -subgroup for all i ∈ I. A subgroup A of G is said to be σ-permutable in G provided G is σ -full and A permutes with all Hall σ i -subgroups H of G (that is, A H = H A) for all i. We obtain a description of finite σ -full groups G with supersoluble Hall σ i -subgroups for all i ∈ I in which σ -permutability is a transitive relation on G. [ABSTRACT FROM AUTHOR]