Automorphisms of iterated wreath product \(p\)-groups. (Q2888793)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Automorphisms of iterated wreath product \(p\)-groups. |
scientific article; zbMATH DE number 6042610
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Automorphisms of iterated wreath product \(p\)-groups. |
scientific article; zbMATH DE number 6042610 |
Statements
4 June 2012
0 references
wreath products
0 references
finite \(p\)-groups
0 references
automorphism groups
0 references
character theory
0 references
finite general linear groups
0 references
orders of groups of automorphisms
0 references
0.9741967
0 references
0.96200824
0 references
0.9559771
0 references
0.94434637
0 references
0.9313525
0 references
0.9276045
0 references
0.9252576
0 references
Automorphisms of iterated wreath product \(p\)-groups. (English)
0 references
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.
0 references
