2014/09/28 by Ali Mahmoudifar, Mahmoudifar, Ali, Behrooz Khosravi +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.GR
paper · pdf · doi:10.48550/arxiv.1409.7903
3 pages
arxiv created 2014/09/28 · openalex publication_date 2014/09/28 · arxiv updated 2014/09/30 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28
In [Akbari and Moghaddamfar, Recognizing by order and degree pattern of some projective special linear groups, \it Internat. J. Algebra Comput., 2012] the authors possed the following problem: \bf Problem. \it Is there a simple group which is k-fold OD-characterizable for k≥3 ? In this paper as the main result we give positive answer to the above problem and we introduce two simple groups which are k-fold OD-characterizable such that k≥6. Also in [R. Kogani-Moghadam and A. R. Moghaddamfar, Groups with the same order and degree pattern, \it Science China Mathematics, 2012], the authors possed two conjectures as follows: \bf Conjecture 1. \it All alternating groups Am with m \not= 10 are OD-characterizable. \bf Conjecture 2. \it All symmetric groups Sm, with m \not= 10, are n-fold OD-characterizable, where n∈\1, 3\. In this paper we find some alternating and some symmetric groups such that these conjectures are not true for them.