【摘 要】
：
For any group G, denote by 7πe(G) the set of orders of elements in G. Given a finite group G, let h(πe(G)) be the number of isomorphism classes of finite grou
【机 构】
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Department of Mathematics and Computer Sciences
【基金项目】
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the Research Institute for Fundamental Sciences Tabriz, Iran
论文部分内容阅读
For any group G, denote by 7πe(G) the set of orders of elements in G. Given a finite group G, let h(πe(G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G is called k-recognizable if h(πe(G)) =k ＜∞, otherwise G is called non-recognizable. Also a 1-recognizable group is called a recognizable (or characterizable) group. In this paper the authors show that the simple groups PSL(3, q), where 3 ＜ q ≡±2 (mod 5) and (6, (q - 1)/2) = 1, are recognizable.
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