OD-CHARACTERIZATION OF ALTERNATING GROUP OF DEGREE p + 3 - Yan, Yanxiong; Zeng, Yu; Xu, Haijing; Chen, Guiyun (Italian Journal of Pure and Applied Mathematics, 2014)
Let Ap+3 be the alternating group of degree p + 3, where p is a prime, p + 4 is a composite number, p + 6 is a prime and 7 ≠ p ∈ π(1000!). In the present paper, we prove that Ap+3 is OD-characterizable by using the classification theorem of finite simple groups and Magma soft of computational group theory. This new method is introduced in order to deal with the subtle changes of the prime graph of a group in the discussion of its OD-characterization, which might occur. As a consequence of this theorem not only generalizes the result in [1] (Hoseini, A.A. and Moghaddamfar, A.R., Frontiers of Mathematics in China, 5 (3), 2010) but also gives a positive answer to a conjecture in [2] (Shi, W.J., Contemporary Math., 82, 1989).