Abstract
We identify M(24) by the structure of the normalizer of a 3-central element. Also as a corollary we identify M(24) by two of its 3-local subgroups.
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References
Aschbacher M., 3-Transposition Groups, Cambridge Univ. Press, Cambridge (1997).
Salarian M. R., “A 3-local characterization of Fi’24,” J. Algebra, vol. 324, 2804–2813 (2010).
Salarian M. R., “A 2-local characterization for M(24)’,” Monatsh. Math., vol. 167, no. 3, 583–588 (2012).
Conway J. H., Curtis R. T., Norton S. P., Parker R. A., and Wilson R. A., Atlas of Finite Groups, Clarendon Press, Oxford 1985).
Aschbacher M., Finite Group Theory, Cambridge Univ. Press, Cambridge 1986).
Meierfrankenfeld U. and Stroth G., Groups of Local Characteristic p. The H-Structure Theorem [Preprint]; http://conway1.mathematik.uni-halle.de/stroth/.
Meierfrankenfeld U., Stellmacher B., and Stroth G., “Finite groups of local characteristic p: An overview,” in: Proc. Durham Conf. Finite Groups, World Sci. Publ., River Edge, NJ, 2003, 1–39.
Parker Ch., “A 3-local characterization of U 6(2) and Fi 22,” J. Algebra, vol. 300, no. 2, 707–728 (2006).
Reifart A., “Some simple groups related to M 24,” J. Algebra, vol. 45, no. 1, 199–209 (1977).
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Karaj/Tehran. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 2, pp. 399–405, March–April, 2017; DOI: 10.17377/smzh.2017.58.213.
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Salarian, M.R. A 3-local characterization of M(24). Sib Math J 58, 305–309 (2017). https://doi.org/10.1134/S0037446617020136
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DOI: https://doi.org/10.1134/S0037446617020136