2-local subgroups of Fischer groups. (Russian) Zbl 0541.20007

Flaass, D. G.

Mat. Zametki 35, No. 3, 333-342 (1984).

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

Keywords:

2-local maximal subgroups; Fischer groups; centralizers of involutions