Abstract
It is proved that a finite group that is isomorphic to a simple non-Abelian group G=G 2(3n) is, up to isomorphism, recognized by a set ω(G) of its element orders, that is, H ≃ G if ω(H)=ω(G) for some finite group H.
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Vasilyev, A.V. Recognizing Groups G 23n) by Their Element Orders. Algebra and Logic 41, 74–80 (2002). https://doi.org/10.1023/A:1015300429047
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DOI: https://doi.org/10.1023/A:1015300429047