2009/12/15 by L. S. Kazarin, Л. С. Казарин, A. Martı́nez-Pastor +6
Computer Science · Mathematics · #20D20 #20E32 #20F17 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras #math.GR #msc:20D20 #msc:20E32 #msc:20F17
paper · pdf · doi:10.48550/arxiv.0912.2839
arxiv created 2009/12/15 · openalex publication_date 2009/12/15 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a finite group and Gp be a Sylow p-subgroup of G for a prime p in π(G), the set of all prime divisors of the order of G. The automiser Ap(G) is defined to be the group NG(Gp)/GpCG(Gp). We define the Sylow graph ΓA(G) of the group G, with set of vertices π(G), as follows: Two vertices p,q∈π(G) form an edge of ΓA(G) if either q∈π(Ap(G)) or p∈ π(Aq(G)). The following result is obtained: Theorem: Let G be a finite almost simple group. Then the graph ΓA(G) is connected and has diameter at most 5. We also show how this result can be applied to derive information on the structure of a group from the normalizers of its Sylow subgroups.