A new characterization of some alternating and symmetric groups

Amir Khosravi and Behrooz Khosravi

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-10

Abstract:

We suppose that p = 2 α 3 β + 1 , where α ≥ 1 , β ≥ 0 , and p ≥ 7 is a prime number. Then we prove that the simple groups A n , where n = p , p + 1 , or p + 2 , and finite groups S n , where n = p , p + 1 , are also uniquely determined by their order components. As corollaries of these results, the validity of a conjecture of J. G. Thompson and a conjecture of Shi and Bi (1990) both on A n , where n = p , p + 1 , or p + 2 , is obtained. Also we generalize these conjectures for the groups S n , where n = p , p + 1 .

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:239416

DOI: 10.1155/S0161171203202386

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