Simple fusion systems over \(p\)-groups with abelian subgroup of index \(p\). I. (Q401756)
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scientific article; zbMATH DE number 6334769
| Language | Label | Description | Also known as |
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| English | Simple fusion systems over \(p\)-groups with abelian subgroup of index \(p\). I. |
scientific article; zbMATH DE number 6334769 |
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Simple fusion systems over \(p\)-groups with abelian subgroup of index \(p\). I. (English)
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27 August 2014
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The simple fusion systems over a finite nonabelian \(p\)-group \(S\) with an abelian subgroup \(A\) of index \(p\) are considered. If \(S\) has another abelian subgroup of index \(p\) the consideration is reduced to a case considered by \textit{A. Ruiz} and \textit{A. Viruel}, [Math. Z. 248, No. 1, 45-65 (2004; Zbl 1062.20022)] (in that case \(S\) is nonabelian of order \(p^3\) and exponent \(p\)). If \(A\) is the unique abelian subgroup of index \(p\) in \(G\) and is not radical in the fusion system, a complete list of all possibilities which can occur is presented.
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finite \(p\)-groups
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simple saturated fusion systems
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exotic fusion systems
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