A 2-local characterization of \(M(24)'\). (Q714962)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A 2-local characterization of \(M(24)'\). |
scientific article; zbMATH DE number 6093467
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A 2-local characterization of \(M(24)'\). |
scientific article; zbMATH DE number 6093467 |
Statements
A 2-local characterization of \(M(24)'\). (English)
0 references
15 October 2012
0 references
The author proves the following theorem. Let \(G\) be a finite group and \(z\) be an involution in \(G\). If \(z\) is not weakly closed in \(O^2(C_G(z))\) with respect to \(G\), then \(G\) is isomorphic to Fischer's 3-transposition group \(M(24)' =Fi_{24}'\). This result is an improvement of the same result by \textit{S. L. Davis} and \textit{R. Solomon} [Commun. Algebra 9, 1725-1742 (1981; Zbl 0472.20007)].
0 references
finite simple groups
0 references
sporadic simple groups
0 references
Fischer groups
0 references
3-transposition groups
0 references
