Abstract
In 1979, Herzog put forward the following conjecture: if two simple groups have the same number of involutions, then they are of the same order. We give a counterexample to this conjecture.
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References
M. Herzog, On the classification of finite simple groups by the number of involutions, Proc. Amer. Math. Soc. 77 (1979), 313–314.
L. J. Taghvasani and M. Zarrin, A characterization of \(A_5\) by its same-order type. Monatsh. Math. 182 (2017), 731–736.
W.J. Wong, A characterization of the finite projective symplectic groups PSp(4,q), Trans. Amer. Math. Soc. 139 (1969), 1–35.
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Zarrin, M. A counterexample to Herzog’s Conjecture on the number of involutions. Arch. Math. 111, 349–351 (2018). https://doi.org/10.1007/s00013-018-1195-8
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DOI: https://doi.org/10.1007/s00013-018-1195-8