TY - JOUR
AU - Dr. Behnam Razzaghmaneshi
PY - 2018/09/30
Y2 - 2024/04/19
TI - Orbits of Permutation Groups
JF - GPH - International Journal of Mathematics
JA - m
VL - 1
IS - 2
SE - Articles
DO -
UR - https://gphjournal.org/index.php/m/article/view/104
AB - Let $G$ be a permutation group on a set $\Omega$ with no fixedpoints in $\Omega$ and let $m$ be a positive integer. If noelement of $G$ moves any subset of $\Omega$ by more than $m$points (that is, if $|\Gamma^g \setminus \Gamma|\leq m$ for every$\Gamma \subseteq \Omega$ and $g\in G$), and the lengths of allorbits are not equal to $2$. Then the number $t$ of $G$-orbits in $\Omega$ is at most $2m-2$. Moreover, the groups attaining the maximum bound $t=2m-2$ will be classified. \vspace{.4cm}\\
ER -