2021/07/27 by Melissa Lee, Lee, Melissa, Tomasz Popiel +1
Engineering · Mathematics · Medicine · #Chronic Lymphocytic Leukemia Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Synthesis of Organic Compounds #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2107.12755
openalex publication_date 2021/07/27 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
The prime graph, or Gruenberg--Kegel graph, of a finite group G is the\ngraph \Γ(G) whose vertices are the prime divisors of |G|, and whose\nedges are the pairs p,q for which G contains an element of order pq.\nA finite group G is recognisable by its prime graph if every finite group H\nwith \Γ(H)=\Γ(G) is isomorphic to G. By a result of Cameron and\nMaslova, every such group must be almost simple, so one natural case to\ninvestigate is that in which G is one of the 26 sporadic simple groups.\nExisting work of various authors answers the question of recognisability by\nprime graph for all but three of these groups, namely the Monster, \M,\nthe Baby Monster, \B, and the first Conway group, \Co1. We\nprove that these three groups are recognisable by their prime graphs.\n