Minimal characteristic bisets and finite groups realizing Ruiz-Viruel exotic fusion systems

Details Minimal characteristic bisets and finite groups realizing Ruiz-Viruel exotic fusion systems Minimal characteristic bisets and finite groups realizing Ruiz-Viruel exotic fusion systems

2010-11-19

arxiv.org/abs/1011.4505v1

Mathematics

Representation Theory

22 pages

Scientific paper

Continuing our previous work, we determine a minimal left characteristic biset $X$ for every exotic fusion system $\mathcal{F}$ on the extraspecial group $S$ of order $7^3$ and exponent $7$ discovered by Ruiz and Viruel, and analyze the finite group $G$ obtained from $X$ which realizes $\mathcal{F}$ as the full subcategory of the $7$-fusion system of $G$. In particular, we obtain an upper bound for the exoticity index for $\mathcal{F}$.

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