Simple fusion systems over \(p\)-groups with abelian subgroup of index \(p\). I.
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.
scientific article; zbMATH DE number 6334769
scientific article