Pure Quantitative Characterization of Finite Simple Groups 2Dn(q) and Dl(q) (l odd)

摘要

Let G be a group and M(q) be one of the Lie type simple groups 2Dn(q) (n ≥ 4) and Dn(q) (n odd, n ≥ 5). In this paper, we prove that G ≌ M(q)if and only if (I) πe(G) = πe(M(q)), where πe(G) is the set of orders of elements in G; and (ii) |G| = |M(q)|.