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Licensed Unlicensed Requires Authentication Published by De Gruyter November 21, 2020

Commuting graph of 𝐴-orbits

  • İsmail Ş. Güloğlu and Gülin Ercan EMAIL logo
From the journal Journal of Group Theory

Abstract

Let 𝐴 be a finite group acting by automorphisms on the finite group 𝐺. We introduce the commuting graph Γ(G,A) of this action and study some questions related to the structure of 𝐺 under certain graph theoretical conditions on Γ(G,A).

Acknowledgements

We thank N. V. Maslova and A. V. Vasil’ev for their valuable comments on our questions about the Grünberg–Kegel graph. Also, we would like to thank anonymous referee for careful reading and valuable suggestions which helped to improve the presentation of this article.

  1. Communicated by: Christopher W. Parker

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Received: 2019-11-11
Revised: 2020-07-16
Published Online: 2020-11-21
Published in Print: 2021-05-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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