The intersection graph of quasinormal subgroups of a group $G$, denoted by $\Gamma_{\mathrm{q}}(G)$, is a graph defined as follows: the vertex set consists of all nontrivial, proper quasinormal subgroups of $G$, and two distinct vertices $H$ and $K$ are adjacent if $H\cap K$ is nontrivial. In this paper, we show that when $G$ is an arbitrary nonsimple group, the diameter of $\Gamma_{\mathrm{q}}(G)$ is in $\{0,1,2,\infty\}$. Besides, all general skew linear groups $\mathrm{GL}_n(D)$ over a division ring $D$ can be classified depending on the diameter of $\Gamma_{\mathrm{q}}(\mathrm{GL}_n(D))$.
division ring general skew linear group intersection graph quasinormal subgroup permutable subgroup
Vietnam National University HoChiMinh City (VNUHCM)
T2022-18-03
This research is funded by Vietnam National University HoChiMinh City (VNUHCM) under grant number T2022-18-03.
T2022-18-03
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Matematik |
Yazarlar | |
Proje Numarası | T2022-18-03 |
Erken Görünüm Tarihi | 15 Ağustos 2023 |
Yayımlanma Tarihi | 23 Nisan 2024 |
Yayımlandığı Sayı | Yıl 2024 Cilt: 53 Sayı: 2 |