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A NEW CHARACTERIZATION OF ALTERNATING AND SYMMETRIC GROUPS
ALAVI, S. H.,DANESHKHAW, A. 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.17 No.1
In this paper we prove that the alternating groups A_n, for n = p, p+1, p+2 and symmetric groups $S_n$, for n = p, p+1, where p$\ge$3 is a prime number, can be uniquely determined by their order components. As one of the important consequence of this characterization we show that the simple groups An, where n = p, p+1, P+2 and p$\ge$3 is prime, satisfy in Thompson's conjecture and Shi's conjecture.