Bob Oliver
Published 2022-04-16Version 1
We study a certain family of simple fusion systems over finite $3$-groups, ones that involve Todd modules of the Mathieu groups $2M_{12}$, $M_{11}$, and $A_6=O^2(M_{10})$ over $\mathbb{F}_3$, and show that they are all isomorphic to the $3$-fusion systems of almost simple groups. As one consequence, we give new $3$-local characterizations of Conway's sporadic simple groups.
Reductions to simple fusion systems
Reduced fusion systems over $p$-groups with abelian subgroup of index $p$: III
Nonrealizability of certain representations in fusion systems
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