Finite groups with odd Sylow normalizers (Q2827363)
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scientific article; zbMATH DE number 6640937
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite groups with odd Sylow normalizers |
scientific article; zbMATH DE number 6640937 |
Statements
Finite groups with odd Sylow normalizers (English)
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19 October 2016
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McKay conjecture
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Alperin weight conjecture
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Sylow normalizers
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The main result of the paper under review is that if the order of the normalizer of a Sylow \(p\)-subgroup of a finite group \(G\) is odd, then any non-abelian composition factor of \(G\) has cyclic Sylow \(p\)-subgroup or is isomorphic to \(\mathrm{PSL}(2,q)\), where \(q\) is congruent to 3 modulo 4 and \(q\) is a power of \(p\). As a consequence, the authors prove the McKay conjecture and the Alperin weight conjecture for these groups at the prime \(p\).
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