CONNECTED COMPONENTS IN THE INVARIABLY GENERATING GRAPH OF A FINITE GROUP

DOI10.1017/S0004972721000149MaRDI QIDQ5013857

Daniele Garzoni

Publication date: 3 December 2021

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.14536

zbMATH Keywords

connected componentsinvariably generating graph

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Arithmetic and combinatorial problems involving abstract finite groups (20D60)

Cites Work

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• The generating graph of finite soluble groups.
• 2-coverings for exceptional and sporadic simple groups.
• Invariable generation and the Chebotarev invariant of a finite group.
• Covers and normal covers of finite groups.
• Invariable generation with elements of coprime prime-power orders.
• Probabilistic generation of finite simple groups. II.
• Random sets which invariably generate the symmetric group
• Probabilistic generation of finite simple groups
• The non-isolated vertices in the generating graph of a direct powers of simple groups.
• Connectivity of generating graphs of nilpotent groups
• The invariably generating graph of the alternating and symmetric groups
• Minimal invariable generating sets
• Normal coverings of linear groups.
• Normal coverings and pairwise generation of finite alternating and symmetric groups.
• Generic \(2\)-coverings of finite groups of Lie type.
• The probability of generating a finite classical group
• The spread of a finite group
• The Maximal Subgroups of the Low-Dimensional Finite Classical Groups
• Simple groups admit Beauville structures
• COVERINGS OF LINEAR GROUPS
• Graphs encoding the generating properties of a finite group
• Simple Groups, Generation and Probabilistic Methods