On the generating graph of a simple group

Andrea Lucchini; Attila Maroti; Colva Mary Roney-Dougal

doi:10.1017/S1446788716000458

On the generating graph of a simple group

Andrea Lucchini, Attila Maroti, Colva Mary Roney-Dougal

Research output: Contribution to journal › Article › peer-review

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 G ≅ H. We also prove that the generating graph of a symmetric group determines the group.

Original language	English
Pages (from-to)	91-103
Journal	Journal of the Australian Mathematical Society
Volume	103
Issue number	1
Early online date	26 Sept 2016
DOIs	https://doi.org/10.1017/S1446788716000458
Publication status	Published - Aug 2017

Keywords

Generating graph
Finite group

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10.1017/S1446788716000458

gengraph_revised_post_submission
© 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
Accepted author manuscript, 280 KB

Colva Roney-Dougal, OBE
- Colva.Roney-Dougalst-andrews.acuk
Person: Academic

Cite this

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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 G ≅ H. We also prove that the generating graph of a symmetric group determines the group.",

keywords = "Generating graph, Finite group",

author = "Andrea Lucchini and Attila Maroti and Roney-Dougal, {Colva Mary}",

note = "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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KW - Finite group

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JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

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On the generating graph of a simple group

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Colva Roney-Dougal, OBE

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