Let G be a finite group and let π e (G) be the set of orders of elements from G. Let k ∈ π e (G) and let m k be the number of elements of order k in G. We set nse (G) := {m k | k ∈ π e (G)}. It is proved that PSL(2, q) are uniquely determined by nse (PSL(2, q)), where q ∈ {5, 7, 8, 9, 11, 13}. As the main result of the paper, we prove that if G is a group such that nse (G) = nse (PSL(2, q)), where q ∈ {16, 17, 19, 23}, then G ≅ PSL(2, q).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 9, pp. 1155–1162, September, 2015.
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Asboei, A.K., Amiri, S.S.S. & Iranmanesh, A. A New Characterization of PSL(2, q) for Some q . Ukr Math J 67, 1297–1305 (2016). https://doi.org/10.1007/s11253-016-1153-1
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DOI: https://doi.org/10.1007/s11253-016-1153-1