OD-characterization of alternating groups Ap+d

Abstract

Let An be an alternating group of degree n. Some authors have proved that A10, A147 and A189 cannot be OD-characterizable. On the other hand, others have shown that A16, A23+4, and A23+5 are OD-characterizable. We will prove that the alternating groups Ap+d except A10, are OD-characterizable, where p is a prime and d is a prime or equals to 4. This result generalizes other results.

Keywords

• order component
• element order
• alternating group
• degree pattern
• prime graph
• simple group
• 20d05
• 20d06
• 20d60