Evgeny Khukhro gave an invited plenary talk at the international conference “Ischia Group Theory 2024”, which took place on 8–13 Aril 2024 in Ischia (Italy). This biennial conference is one of the major events in the academic calendar attracting experts in group theory from all over the world. Evgeny reported on his joint results with Cristina Acciarri, Robert Guralnick, and Pavel Shumyatsky.