Large minimal invariable generating sets in the finite symmetric groups

Garzoni, Daniele and Gill, Nick (2023). Large minimal invariable generating sets in the finite symmetric groups. Israel Journal of Mathematics, 255 pp. 581–598.

DOI: https://doi.org/10.1007/s11856-023-2467-y

Abstract

For a finite group G, let m_I(G) denote the largest possible cardinality of a minimal invariable generating set of G. We prove an upper and a lower bound for m_I(S_n), which show in particular that m_I(S_n) is asymptotic to n/2 as n → ∞.

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