Automorphisms of iterated wreath product \(p\)-groups.
Let \(W=(\cdots((\mathbb Z_{p^e}\wr\mathbb Z_p)\wr\mathbb Z_p)\cdots\wr\mathbb Z_p)\) be an (\(n\) times) iterated regular wreath product, well-known to be isomorphic to a \(p\)-Sylow subgroup of the linear group \(\text{GL}_{p^{{n-1}}}(q)\), where \(p\mid q-1\), and the \(p\)-part of \(q-1\) is \(p^e\geq 3\). The author determines the order of the automorphism group \(\Aut(W)\) using a method based on representation theory, namely, the author's automorphism counting formula [J. Algebra 322, No. 12, 4483-4497 (2009; Zbl 1193.20026)].NEWLINENEWLINE In the second part of the paper several properties of characters of the group \(W\) are established.
scientific article; zbMATH DE number 6042610