A variation on the Glauberman correspondence (Q1860774)
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scientific article; zbMATH DE number 1874595
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A variation on the Glauberman correspondence |
scientific article; zbMATH DE number 1874595 |
Statements
A variation on the Glauberman correspondence (English)
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16 November 2003
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Let \(G\) be a finite \(p\)-solvable group. Let \(P\) be a Sylow \(p\)-subgroup of \(G\). Let \(\text{IBr}(G)\) be the set of irreducible Brauer characters of \(G\) and \(\text{IBr}_{p'}(G)\) be the set of those \(\varphi\in\text{IBr}(G)\) such that \(p\nmid\varphi(1)\). The main result of the paper under review is that when \(N_G(P)\) has a normal \(p\)-complement, then there is a bijection between \(\text{IBr}_{p'}(G)\) and \(\text{IBr}(N_G(P))\).
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Glauberman correspondence
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finite \(p\)-solvable groups
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Sylow subgroups
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irreducible Brauer characters
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normal complements
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0.8342046737670898
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0.8291473388671875
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0.8253150582313538
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