Isomorphic character tables of nested \(GVZ\)-groups. (Q2885394)
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scientific article; zbMATH DE number 6037681
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Isomorphic character tables of nested \(GVZ\)-groups. |
scientific article; zbMATH DE number 6037681 |
Statements
23 May 2012
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finite \(p\)-groups
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character tables
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irreducible characters
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homogeneous character induction
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Isomorphic character tables of nested \(GVZ\)-groups. (English)
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The notion of nested \(GVZ\)-groups is introduced. Necessary and sufficient conditions for two non-isomorphic nested \(GVZ\)-groups to have isomorphic character tables are provided.NEWLINENEWLINE As to the definition of \(GVZ\)-group: A non-Abelian group \(G\) is called a \(GVZ\)-group if for all \(\chi\in\text{Irr}(G)\), \(\chi(g)=0\) for all \(g\in G\setminus Z(\chi)\); here \(Z(\chi)\) stands for \(\{u\in G\mid|\chi(u)|=\chi(1)\}\). These groups are strongly connected with the finite groups occurring in the papers of \textit{E. B. Kuisch} and \textit{R. W. van der Waall} [J. Algebra 149, No. 2, 454-471 (1992; Zbl 0774.20005) and ibid. 170, No. 2, 584-595 (1994; Zbl 0817.20020)] and \textit{E. B. Kuisch} [ibid. 156, No. 2, 395-406 (1993; Zbl 0782.20010)].
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