A generalization of the diameter bound of Liebeck and Shalev for finite\n simple groups

2020/03/31 by Attila Maróti, Maróti, Attila, László Pyber +1 · 1 citation
Engineering · Mathematics · #20D06 #20D40 #20G05 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2003.14270

openalex publication_date 2020/03/31 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

Let G be a non-abelian finite simple group. A famous result of Liebeck and\nShalev is that there is an absolute constant c such that whenever S is a\nnon-trivial normal subset in G then S^k = G for any integer k at least\nc \⋅ (\log|G|/\log|S|). This result is generalized by showing that there\nexists an absolute constant c such that whenever S₁, \… , S_k are\nnormal subsets in G with \∏_i=1^k |S_i| \≥ |G|^c then S₁\n\⋯ S_k = G.\n

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