Every group is the automorphism group of a graph with arbitrarily large genus

2025/01/15 by Marco Barbieri, Barbieri, Marco
Mathematics · #05C10 #05C25 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2501.08747

openalex publication_date 2025/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that, to every abstract group G, we can associate a sequence of graphs Γ_n such that the automorphism group of Γ_n is isomorphic to G and the genus of Γ_n is an unbounded function of n.

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