The non-two-primes graph of a finite group

Articles in Press

Document Type : Research Paper

Authors

Dipartimento di Matematica “Tullio Levi Civita”, Università di Padova, Via Trieste 63, 35121 Padova, Italy

Abstract

To any finite group $G$, we may associate a graph whose vertices are the elements of $G$ and where two distinct vertices $x$ and $y$ are adjacent if and only if the order of the subgroup $\langle x, y\rangle$ is divisible by at least 3 distinct primes. We prove that the subgraph of this graph induced by the non-isolated vertices is connected and has diameter at most 5.

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References

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Transactions on Combinatorics

Articles in Press, Corrected Proof
Available Online from 03 January 2025

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History

  • Receive Date: 07 August 2024
  • Revise Date: 30 December 2024
  • Accept Date: 03 January 2025
  • Published Online: 03 January 2025

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