Finite groups whose automorphism group has order cubefree (Q1364960)

As a step towards the classification of the finite groups \(G\) for which \(|\Aut(G)|\) is cube-free, the author proves the following result: If \(|\Aut(G)|\) is cube-free, then \(G\) possesses the Sylow tower property. Moreover, it is shown that if \(|\Aut(G)|\) is cube-free and odd, then \(|G|\leq 2\). The proof of the main result is based on a number of useful lemmas which ensure the existence of automorphisms with prescribed properties for various group configurations.