Irredundant generating sets and dimension-like invariants of the finite group

2017/12/11 by Minh Nguyen, Nguyen, Minh
Materials Science · #FOS: Mathematics #Group Theory (math.GR) #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.1712.03923

openalex publication_date 2017/12/11 · openalex created_date 2017/12/22 · openalex updated_date 2026/07/28

Abstract

Whiston proved that the maximum size of an irredundant generating set in the symmetric group S_n is n-1, and Cameron and Cara characterized all irredundant generating sets of S_n that achieve this size. Our goal is to extend their results. Using properties of transitive subgroups of the symmetric group, we are able to classify all irredundant generating sets with sizes n-2 in both A_n and S_n. Next, based on this classification, we derive other interesting properties for the alternating group A_n. Finally, using Whiston's lemma, we will derive the formulas for calculating dimension-like invariants of some specific types of wreath products.

Citations

• On an Inequality of Dimension-like Invariants for Finite Groups

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• On an Inequality of Dimension-like Invariants for Finite Groups