The probability that two elements of a group have the same centralizers

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, University of Kurdistan, P.O. Box 416, Sanandaj, Kurdistan, Iran

2 Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX, 78666, USA

Abstract

In this paper we provide some bounds for the probability, denoted by $\mathcal{PC}(G)$, that two randomly chosen elements in a given finite group have the same centralizers. In particular, among other results, we give the following best possible bounds for $\mathcal{PC}(G)$, depending only on $|G:Z(G)|$ and the smallest prime divisor of $|G|$.

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References

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International Journal of Group Theory

Articles in Press, Corrected Proof
Available Online from 11 November 2024

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History

  • Receive Date: 22 July 2024
  • Revise Date: 28 September 2024
  • Accept Date: 30 September 2024
  • Published Online: 11 November 2024

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