Finite soluble groups satisfying the replacement property

2017/10/02 by Andrea Lucchini, Lucchini, A.
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1710.00582

openalex publication_date 2017/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the finite soluble groups G with the following property (replacement property): for every irredundant generating set \g₁,…,g_m\ of maximal size and for any 1≠ g∈ G there exists an i∈ \1,…,m\ so that ⟨ g₁,…,g_i-1,g,g_i+1,…,g_m⟩=G.

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