On the generating graph of a simple group
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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 G ≅ H. We also prove that the generating graph of a symmetric group determines the group.
Lucchini , A , Maroti , A & Roney-Dougal , C M 2016 , ' On the generating graph of a simple group ' Journal of the Australian Mathematical Society , vol First View . DOI: 10.1017/S1446788716000458
Journal of the Australian Mathematical Society
© 2016 Australian Mathematical Publishing Association Inc. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at: https://doi.org/10.1017/S1446788716000458
The authors were supported by Universita di Padova (Progetto di Ricerca di Ateneo: Invariable generation of groups). The second author was also supported by an Alexander von Humboldt Fellowship for Experienced Researchers, by OTKA grants K84233 and K115799, and by the MTA Renyi Lendulet Groups and Graphs Research Group.
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