On automorphisms of \(A\)-groups.
A group \(G\) is said to be an \(A\)-group if \(xx^\alpha=x^\alpha x\) for all \(a\in G\) and \(\alpha\in\Aut(G)\). Let \(A_C(G)\) denote the subgroup of \(\Aut(G)\) consisting of all automorphisms that leave invariant the centralizer of each element of \(G\). By \(\Aut_c(G)\) we denote the group of all central automorphisms of \(G\). The quotient \(\Aut(G)/\Aut_c(G)\) has exponent at most \(2\). The main result of this interesting paper is the following Theorem 1.1. Let \(r\) be a positive integer and \(p>2\) a prime. Then there exist infinitely many finite \(p\)-groups \(G\) such that \(G\) is an \(A\)-group, \(A_C(G)=\Aut_c(G)\) and the elementary Abelian \(2\)-group \(\Aut(G)/\Aut_c(G)\) has order \(2^r\).
scientific article; zbMATH DE number 5500767