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16.24 (2006)

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The spectrum of a finite group is the set of orders of its elements. Does there exist a finite group $G$ whose spectrum coincides with the spectrum of a finite simple exceptional group $L$ of Lie type, but $G$ is not isomorphic to $L$?

Contributor: A. V. Vasil'ev

Progress

Yes, for example, for $L = {}^3D_4(2)$ (V. D. Mazurov, Algebra Logic, 52, no. 5 (2013), 400–403). Further examples are given in M. A. Grechkoseeva, M. A. Zvezdina, J. Algebra Appl., 15, no. 9 (2016), Article ID 1650168, 13 pp.).

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