Finite groups with its power automorphism groups having small indices.
The paper studies those finite groups \(G\) for which \(|\Aut(G):P(G)|\) is small, where \(P(G)\) is the group of power automorphisms of \(G\). It is shown that \(|\Aut(G):P(G)|\) cannot be a prime. Also, \(|\Aut(G):P(G)|\) is the product of two distinct primes precisely when \(G\) is the direct product of a cyclic group \(A\) with a group \(B\) of coprime order and very restricted (and completely determined) structure.
scientific article; zbMATH DE number 5601606
scientific article