• Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/122/02/0175-0179

    • Keywords

       

      Permutation group; bounded movement; orbit.

    • Abstract

       

      Let 𝐺 be a permutation group on a set 𝛺 with no fixed points in 𝛺 and let 𝑚 be a positive integer. If no element of 𝐺 moves any subset of 𝛺 by more than 𝑚 points (that is, $|\Gamma^g\backslash\Gamma|\leq m$ for every $\Gamma\subseteq\Omega$ and $g\in G$), and also if each 𝐺-orbit has size greater than 2, then the number 𝑡 of 𝐺-orbits in 𝛺 is at most $\frac{1}{2}(3m-1)$. Moreover, the equality holds if and only if 𝐺 is an elementary abelian 3-group.

    • Author Affiliations

       

      Mehdi Alaeiyan1 Behnam Razzaghmaneshi1

      1. Department of Mathematics, Islamic Azad University-Karaj Branch, Karaj, Iran
    • Dates

       
  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2021-2022 Indian Academy of Sciences, Bengaluru.