On the Covering Number of U₃(q)

2021/05/17 by Michael P. Epstein, Epstein, Michael
Mathematics · #20D60 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Group Theory (math.GR) #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2105.08183

openalex publication_date 2021/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The covering number, σ(G), of a finite, noncyclic group G is the least positive integer n such that G is the union of n proper subgroups. Here we investigate the covering numbers of the projective special unitary groups U₃(q), give upper and lower bounds for σ(U₃(q)) when q ≥ 7, and show that σ(U₃(q)) is asymptotic to q⁶/3 as q → ∞.

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