Covers and Normal Covers of Finite Groups

2013/10/07 by Andrea Lucchini, Martino Garonzi, Lucchini, Andrea +1 · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.GR

paper · pdf · doi:10.48550/arxiv.1310.1775

arxiv created 2013/10/07 · openalex publication_date 2013/10/07 · arxiv updated 2013/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a finite non cyclic group G, let γ(G) be the smallest integer k such that G contains k proper subgroups H₁,…,H_k with the property that every element of G is contained in H_i^g for some i ∈ \1,…,k\ and g ∈ G. We prove that if G is a noncyclic permutation group of degree n, then γ(G)≤ (n+2)/2. We then investigate the structure of the groups G with γ(G)=σ(G) (where σ(G) is the size of a minimal cover of G) and of those with γ(G)=2.

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