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2-local subgroups of Fischer groups. (Russian) Zbl 0541.20007
The purpose of the paper under review is to describe all the 2-local maximal subgroups of the Fischer groups $$F_{22}$$ and $$F_{23}$$.
Theorem. Let $$G$$ be a finite group and $$L$$ be a maximal subgroup with $$O_ 2(L)\neq 1.$$
(a) If $$G=F_{22}$$ then $$L$$ is isomorphic to one of the following groups:
$$Z_ 2\backslash U_ 6(2),\;(Z_ 2\times Q^ 4)\backslash U_ 4(2)\backslash Z_ 2$$ (centralizers of involutions), $$E_{2^{10}}\cdot M_{22},\;E_{2^ 9}\backslash E_{2^ 4}\backslash A_ 6\backslash \Sigma_ 3,\;E_{2^ 6}S_ 6(2)$$.
(b) If $$G=F_{23}$$ then $$L$$ is isomorphic to one of the following:
$$Z_ 2\backslash F_{22},\;E_ 4\backslash U_ 5(2),\;(E_ 4\times Q^ 4)\backslash(Z_ 3\times U_ 4(2))\backslash Z_ 2$$ (centralizers of involutions), $$\Sigma_ 4\times S_ 6(2)$$,
$$E_{2^{11}}\backslash M_{23},\;E_{2^{10}}\backslash E_{16}\backslash A_ 7\backslash \Sigma_ 3$$.
Note that R. A. Wilson [J. Algebra 84, 107–114 (1983; Zbl 0524.20007)] using the classification of finite simple groups proved a stronger fact than part (a) for $$F_{22}$$.
Reviewer: S. A. Syskin

##### MSC:
 20D05 Finite simple groups and their classification 20D08 Simple groups: sporadic groups 20D30 Series and lattices of subgroups
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