Groups of p-rank 2 containing an isolated element of order p

Let p be an odd prime and G be a finite group with O p ′ ( G ) = 1 of p -rank at most 2 that contains an isolated element of order p . If x ∉ Z ( G ) , we show that F ∗ ( G ) is simple and we describe the structure of a Sylow p -subgroup P of F ∗ ( G ) as well as the fusion system F P ( F ∗ ( G ) )...

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Bibliographic Details
Published inArchiv der Mathematik Vol. 118; no. 4; pp. 349 - 359
Main Author Toborg, Imke
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2022
Springer Nature B.V
Subjects
Group theory
Mathematics
Mathematics and Statistics
Subgroups
theorem
20D20
Finite groups
Isolated elements
rank
20D05
Local analysis
Control of fusion
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Summary:Let p be an odd prime and G be a finite group with O p ′ ( G ) = 1 of p -rank at most 2 that contains an isolated element of order p . If x ∉ Z ( G ) , we show that F ∗ ( G ) is simple and we describe the structure of a Sylow p -subgroup P of F ∗ ( G ) as well as the fusion system F P ( F ∗ ( G ) ) without using the classification of finite simple groups.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-022-01703-7