论文标题
一般偏度线性组中几乎亚正态亚组的交点图
Intersection graphs of almost subnormal subgroups in general skew linear groups
论文作者
论文摘要
令$ d $为一个分区环，$ n $ a正整数，而gl $ _n（d）$ $ n $ n $ the $ d $的通用线性组。在本文中，我们研究了由GL $ _n（d）$的所有非平凡的几乎适当的几乎亚正态亚组生成的GL $ _n（d）$的相交图的诱导子图。我们表明，如果该子图是非零子，则该子图将完成。该特性将用于研究分区环的亚组结构。特别是，我们证明了一个分区环$ d $的乘法组$ d^*$的每个非中央亚正常子组都包含一个非中央亚正常亚组为$ d^*$。
Let $D$ be a division ring, $n$ a positive integer, and GL$_n(D)$ the general linear group of degree $n$ over $D$. In this paper, we study the induced subgraph of the intersection graph of GL$_n(D)$ generated by all non-trivial proper almost subnormal subgroups of GL$_n(D)$. We show that this subgraph is complete if it is non-null. This property will be used to study subgroup structure of a division ring. In particular, we prove that every non-central almost subnormal subgroup of the multiplicative group $D^*$ of a division ring $D$ contains a non-central subnormal subgroup of $D^*$.
