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Characterization by Intersection Graph of Some Families of Finite Nonsimple Groups

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Abstract

For a finite group G, Γ(G), the intersection graph of G, is a simple graph whose vertices are all nontrivial proper subgroups of G and two distinct vertices H and K are adjacent when H ∩ K ≠ 1. In this paper, we classify all finite nonsimple groups whose intersection graphs have a leaf and also we discuss the characterizability of them using their intersection graphs.

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Acknowledgements

The authors are very thankful to Professor Derek Holt for his great help and valuable comments.

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Authors and Affiliations

  1. Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, Tehran, 15914, Iran

    Hossein Shahsavari & Behrooz Khosravi

Authors
  1. Hossein Shahsavari
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  2. Behrooz Khosravi
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Correspondence to Behrooz Khosravi.

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Shahsavari, H., Khosravi, B. Characterization by Intersection Graph of Some Families of Finite Nonsimple Groups. Czech Math J 71, 191–209 (2021). https://doi.org/10.21136/CMJ.2020.0250-19

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  • DOI: https://doi.org/10.21136/CMJ.2020.0250-19

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