On the group of automorphisms of finite wreath products. (Q2504984)

Summary: We study the structure of the group of automorphisms of the wreath product \(A\text{\,wr\,}C_2\), where \(A\) is a finite nilpotent group, and \(C_2\) is the cyclic group of order 2. In particular we give necessary and sufficient conditions for \(\Aut(A\text{\,wr\,}C_2)\) to be supersolvable depending only on \(\Aut(A)\) and on the Remak decomposition of \(A\).