Simple fusion systems over \(p\)-groups with abelian subgroup of index \(p\). I.
type: Item
instance of: scholarly article
title: Simple fusion systems over \(p\)-groups with abelian subgroup of index \(p\). I.
zbMATH Open document ID: 1323.20017
published in: Journal of Algebra
publication date: 2014-08-27T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 55R35
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 6334769
zbMATH Keywords: finite \(p\)-groups
zbMATH Keywords: simple saturated fusion systems
zbMATH Keywords: exotic fusion systems
author: Bob Oliver
reviewed by: Yakov Berkovich
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2013.09.012
OpenAlex ID: W4242027968
cites work: Reduced, tame and exotic fusion systems
cites work: Fusion systems and amalgams.
cites work: Q3114249
cites work: Q5475463
cites work: Extensions of $p$-local finite groups
cites work: Q3077959
cites work: All 𝑝-local finite groups of rank two for odd prime 𝑝
cites work: Q5577154
cites work: The local structure of finite groups of characteristic 2 type
cites work: Q4375273
cites work: The maximal subgroups of the Steinberg triality groups \(3D_ 4(q)\) and their automorphism groups
cites work: Subgroups of Maximal Rank in Finite Exceptional Groups of Lie Type
cites work: The maximal subgroups of \({}^ 2F_ 4(q^ 2)\)
cites work: Splitting fusion systems over 2-groups
cites work: Saturated fusion systems over $2$-groups
cites work: Frobenius categories.
cites work: The classification of \(p\)-local finite groups over the extraspecial group of order \(p^3\) and exponent \(p\).
DOI: 10.1016/J.JALGEBRA.2013.09.012
description: scientific article; zbMATH DE number 6334769