A \(ZJ\)-theorem for \(p^*,p\)-injectors in finite groups (Q1199653)
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scientific article; zbMATH DE number 94564
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A \(ZJ\)-theorem for \(p^*,p\)-injectors in finite groups |
scientific article; zbMATH DE number 94564 |
Statements
A \(ZJ\)-theorem for \(p^*,p\)-injectors in finite groups (English)
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16 January 1993
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The paper contains the analogous to \textit{G. Glauberman}'s theorems [Can. J. Math. 20, 1101-1135 (1968; Zbl 0164.02202)] with the subgroups \(ZJ(K)\) and \(ZJ^*(K)\) where \(K\) is a \(p^*,p\)-injector of a group. Every group \(G\) possesses \(p^*,p\)-injectors which are the subgroups of the form \(O_{p*}(G)P\), where \(P\) is from the set of Sylow \(p\)-subgroups of \(G\), as proved \textit{M. J. Iranzo} and \textit{M. Torres} [Rend. Semin. Mat. Univ. Padova 82, 233-237 (1989; Zbl 0707.20011)].
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\(p^*,p\)-injectors
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Sylow \(p\)-subgroups
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