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On the generating graph of a simple group

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Author(s)

Andrea Lucchini, Attila Maroti, Colva Mary Roney-Dougal

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Abstract

The generating graph Γ(H) of a finite group H is the graph defined on the elements of H, with an edge between two vertices if and only if they generate H. We show that if H is a sufficiently large simple group with Γ(G) ≅ Γ(H) for a finite group G, then GH. We also prove that the generating graph of a symmetric group determines the group.
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Original languageEnglish
Pages (from-to)91-103
JournalJournal of the Australian Mathematical Society
Volume103
Issue number1
Early online date26 Sep 2016
DOIs
StatePublished - Aug 2017

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