On the generating graph of a simple group
Date
08/2017Metadata
Show full item recordAbstract
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.
Citation
Lucchini , A , Maroti , A & Roney-Dougal , C M 2017 , ' On the generating graph of a simple group ' , Journal of the Australian Mathematical Society , vol. 103 , no. 1 , pp. 91-103 . https://doi.org/10.1017/S1446788716000458
Publication
Journal of the Australian Mathematical Society
Status
Peer reviewed
ISSN
1446-7887Type
Journal article
Description
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.Collections
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