OD-CHARACTERIZATION OF ALTERNATING GROUP OF DEGREE p + 3

Abstract

Let A_p+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 A_p+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).