On a question of Beidleman and Robinson
In (1, Theorem A), Beidleman and Robinson proved that if a group satisfies the permutizer condition, it is soluble, its chief factors have order a prime number or 4 and G induces the full group of automorphisms in the chief factors of order 4. In this paper, we show that the converse of this theorem is false by showing some counterexamples. We also find some sufficient conditions for a group satisfying the converse of that theorem to satisfy the permutizer condition.
Ballester Bolinches, Adolfo Esteban Romero, Ramón 2002 On a question of Beidleman and Robinson Communications in Algebra 30 12 5757 5770