On Diameters of Cayley Graphs over Matrix Groups

2024/09/11 by Porat, Eitan
Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2409.06929

openalex publication_date 2024/09/11 · openalex created_date 2024/10/22 · openalex updated_date 2026/07/28

Abstract

We establish for the matrix group G=SL_n(\mathbbF_p) that there exist absolute constants c∈(0,1) and C>0 such that any symmetric generating set A, with |A|≥|G|^1-c has a covering number ≤ Cn². This result is sharp up to the value of the constant C>0.

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