A Noncoprime Shult Type Theorem.
In this note we study finite -groups admitting a factorization by an Abelian subgroup and a subgroup . As a consequence of our results we prove that if contains an Abelian subgroup of index then has derived length at most .
Let be a loop such that is square-free and the inner mapping group is nilpotent. We show that is centrally nilpotent of class at most two.
Un gruppo finito ciclico-per-nilpotente appartiene alla minima classe di Fitting normale se e solo se è nilpotente.