Automorphisms of regular wreath product \(p\)-groups. (English) Zbl 1189.20025
Summary: We present a useful new characterization of the automorphisms of the regular wreath product group \(P\) of a finite cyclic \(p\)-group by a finite cyclic \(p\)-group, for any prime \(p\), and we discuss an application. We also present a short new proof, based on representation theory, for determining the order of the automorphism group \(\operatorname{Aut}(P)\), where \(P\) is the regular wreath product of a finite cyclic \(p\)-group by an arbitrary finite \(p\)-group.
MSC:
| 20D45 | Automorphisms of abstract finite groups |
| 20D15 | Finite nilpotent groups, \(p\)-groups |
| 20E22 | Extensions, wreath products, and other compositions of groups |
| 20B25 | Finite automorphism groups of algebraic, geometric, or combinatorial structures |
| 20D60 | Arithmetic and combinatorial problems involving abstract finite groups |
References:
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