Affiliation:
1. Université Sorbonne Paris Nord , LAGA, UMR 7539 du CNRS, 99, Av. J.-B. Clément, 93430 Villetaneuse , France
Abstract
Abstract
We study a certain family of simple fusion systems over finite 3-groups, ones that involve Todd modules of the Mathieu groups
2
M
12
2M_{12}
,
M
11
M_{11}
, and
A
6
=
O
2
(
M
10
)
A_{6}=O^{2}(M_{10})
over
F
3
\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.
Subject
Algebra and Number Theory
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