On Hawkes's conjecture for radical classes (Q1357970)

For soluble formations of finite groups, Hawkes established that every totally local formation \({\mathcal F}\) is hereditary and radical and conjectured that the totally local formations are exactly the hereditary radical saturated formations. The author validates Hawkes' conjecture for soluble radical classes, proving that a soluble radical class is totally local if and only if it is hereditary.