Öz
Kaynakça
- [1] M. Alaeiyan and B. Askari, Transitive permutation groups with elements of movement m or m − 1, Math. Reports, 14 (64), 317-324, 2012.
Öz
Let $G$ be a permutation group on a set $\Omega$. Then for each $g\in G$, we define the movement of $g$, denoted by $\move(g)$, the maximal cardinality $|\Delta^{g}\backslash \Delta|$ of $\Delta^{g}\backslash \Delta$ over all subsets $\Delta$ of $\Omega$. And the movement of $G$ is defined as the maximum of $\move(g)$ over all $g\in G$, denoted by $\move(G)$. A permutation group $G$ is said to have bounded movement if it has movement bounded by some positive integer $m$, that is $\move(G)\leq m$. In this paper, we consider the finite transitive permutation groups $G$ with movement $\move(G)=m$ for some positive integer $m>4$, where $G$ is not a $2$-group but in which every non-identity element has the movement $m$ or $m-4$, and there is at least one non-identity element that has the movement $m-4$. We give a characterization for elements of $G$ in Theorem\ref{thm-1}. Further, we apply Theorem \ref{thm-1} to character transitive permutation group $G$ in Theorem \ref{thm-2}. These results give a partial answer to the open problem posed by the authors in 2024.
Anahtar Kelimeler
transitive permutation group movement action non-identity element $p$-group
Kaynakça
- [1] M. Alaeiyan and B. Askari, Transitive permutation groups with elements of movement m or m − 1, Math. Reports, 14 (64), 317-324, 2012.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Grup Teorisi ve Genellemeler |
| Bölüm | Matematik |
| Yazarlar | |
| Erken Görünüm Tarihi | 11 Nisan 2025 |
| Yayımlanma Tarihi | |
| Gönderilme Tarihi | 5 Kasım 2024 |
| Kabul Tarihi | 23 Mart 2025 |
| Yayımlandığı Sayı | Yıl 2025 Erken Görünüm |