Homology, Homotopy and Applications

Volume 25 (2023)

Number 2

Sharpness of saturated fusion systems on a Sylow $p$-subgroup of $\mathrm{G}_2 (p)$

Pages: 329 – 342

DOI: https://dx.doi.org/10.4310/HHA.2023.v25.n2.a14

Authors

Valentina Grazian (Department of Mathematics and Applications, University of Milano–Bicocca, Milano, Italy)

Ettore Marmo (Department of Mathematics and Applications, University of Milano–Bicocca, Milano, Italy)

Abstract

We prove that the Díaz–Park sharpness conjecture holds for saturated fusion systems defined on a Sylow $p$-subgroup of the group $\mathrm{G}_2 (p)$, for $p \geqslant 5$.

Keywords

sharpness, homology decomposition, classifying space, fusion system, Mackey functor

2010 Mathematics Subject Classification

20D20, 20J06, 55R35, 55R40

Full Text (PDF format)

Received 4 October 2022

Received revised 9 November 2022

Accepted 20 November 2022

Published 22 November 2023