TY  - Type of reference 
TI  - [FORTHCOMING] Permutation groups with two orbits having constant movement 
AU  - Mehdi Rezaei
 
AU  - Mehdi Alaeiyan 
AB  - Let $$$G$$$ be a permutation group on a set $$$\Omega$$$ with no fixed points in $$$\Omega$$$, and let $$$m$$$ be a positive integer. If for each subset $$$\Gamma$$$ of $$$\Omega$$$ the size $$$\Gamma^{g}-\Gamma|$$$ is bounded, for $$$g\in G$$$, the movement of $$$g$$$ is defined as move $$$(g):=\max{|\Gamma^{g}-\Gamma|}$$$ over all subsets $$$\Gamma$$$ of $$$\Omega$$$, and move $$$(G)$$$ is defined as the maximum of move $$$(g)$$$ over all non-identity elements of $$$g\in G$$$. Suppose that $$$G$$$ is not a 2-group. It was shown by Praeger that $$$|\Omega|\leqslant\lceil\frac{2mp}{p-1}\rceil+t-1$$$, where $$$t$$$ is the number of $$$G$$$-orbits on $$$\Omega$$$ and $$$p$$$ is the least odd prime dividing $$$|G|$$$. In this paper, we classify all permutation groups with maximum possible degree $$$|\Omega|=\lceil\frac{2mp}{p-1}\rceil+t-1$$$ for $$$t=2$$$, in which every non-identity element has constant movement $$$m$$$. 
DO  - TBA 
JF  - Advances in Pure and Applied Mathematics 
KW  - Intransitive permutation groups, orbits, bounded movement, constant movement., Intransitive permutation groups, orbits, bounded movement, constant movement,  
L1  -  
LA  - en 
PB  - ISTE OpenScience 
DA  - 2024/08/7 
SN  - 1869-6090 
TT  - [FORTHCOMING] Groupe de permutations avec deux orbites à mouvement constant 
UR  - https://openscience.fr/Permutation-groups-with-two-orbits-having-constant-movement 
IS  - Forthcoming papers<br> 
VL  -  
ER  -