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

• Published in: Archiv der Mathematik Vol. 118; no. 4; pp. 349 - 359
• Main Author: Toborg, Imke
• Format: Journal Article
• Language: English
• 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

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 ) )...