A 3-local characterization of \(Fi_{24}'\).
A characterization of the third Fischer group \(Fi'_{24}\) by the structure of the centralizer of a 3-central element is given. As a corollary this group is identified from two of its 3-locals. This corollary has application in the ongoing project of \textit{U. Meierfrankenfeld, B. Stellmacher} and \textit{G. Stroth} to classify the groups of local characteristic \(p\) [Groups, combinatorics and geometry. Proceedings of the L.M.S. Durham symposium, Durham, 2001. River Edge, NJ: World Scientific. 155-192 (2003; Zbl 1031.20008)]. Also the corollary has played a crucial role in the paper by the author and \textit{G. Stroth} [J. Algebra 323, No. 4, 1186-1195 (2010; Zbl 1195.20015)] for identifying the Monster from two of its 3-locals.
scientific article; zbMATH DE number 5840421
scientific article