OD-characterization of alternating groups Ap+d

Abstract

Let A n be an alternating group of degree n. Some authors have proved that A 10 , A 147 and A 189 cannot be OD-characterizable. On the other hand, others have shown that A 16 ; A 23C4 , and A 23C5 are OD-characterizable. We will prove that the alternating groups A pCd except A 10 , are OD-characterizable, where p is a prime and d is a prime or equals to 4. This result generalizes other results.