• Permutation Groups with Bounded Movement having Maximum Orbits

• # Fulltext

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

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

• # Proceedings – Mathematical Sciences

Volume 131, 2021
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• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019

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