2015/04/30 by A. R. Moghaddamfar, Ali Reza Moghaddamfar · 4 citations
Computer Science · Engineering · Mathematics · #Abelian group #Coding theory and cryptography #Combinatorics #Covering groups of the alternating and symmetric groups #Cyclic group #Finite Group Theory Research #Mathematics #Non-abelian group #Pure mathematics #graph theory and CDMA systems #math.GR
paper · pdf · doi:10.1142/s0219498817500657
published in Journal of Algebra and Its Applications 16(04), 1750065 (World Scientific)
openalex publication_date 2016/03/30 · arxiv created 2017/05/24 · arxiv updated 2017/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let [Formula: see text] be the prime graph associated with a finite group [Formula: see text] and [Formula: see text] be the degree pattern of [Formula: see text]. A finite group [Formula: see text] is said to be [Formula: see text]-fold [Formula: see text]-characterizable if there exist exactly [Formula: see text] nonisomorphic groups [Formula: see text] such that [Formula: see text] and [Formula: see text]. The purpose of this paper is two-fold. First, it shows that the symmetric group [Formula: see text] is [Formula: see text]-fold [Formula: see text]-charaterizable. Second, it shows that there exist many infinite families of alternating and symmetric groups, [Formula: see text] and [Formula: see text], which are [Formula: see text]-fold [Formula: see text]-characterizable with [Formula: see text].