Fusion systems over a Sylow $p$-subgroup of $\mathrm{G}_2(p)$

Chris Parker; Jason Semeraro

Fusion systems over a Sylow $p$-subgroup of $\mathrm{G}_2(p)$

Group Theory 2017-07-05 v2

Authors: Chris Parker , Jason Semeraro

Abstract

For $S$ a Sylow $p$ -subgroup of the group $\mathrm{G}_2(p)$ for $p$ odd, up to isomorphism of fusion systems, we determine all saturated fusion systems $\mathcal{F}$ on $S$ with $O_p(\mathcal{F})=1$ . For $p \ne 7$ , all such fusion systems are realized by finite groups whereas for $p=7$ there are $29$ saturated fusion systems of which $27$ are exotic.

Keywords

fusion systems Sylow p-subgroup G2(p) saturated fusion systems exotic fusion systems finite groups

Cite

@article{arxiv.1608.08399,
  title  = {Fusion systems over a Sylow $p$-subgroup of $\mathrm{G}_2(p)$},
  author = {Chris Parker and Jason Semeraro},
  journal= {arXiv preprint arXiv:1608.08399},
  year   = {2017}
}

Comments

30 pages

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