论文标题
恩格尔图的恩格尔图
The Engel graph of a finite group
论文作者
论文摘要
对于有限的组$ g，$我们调查了直接图$γ（g），其顶点是$ g $的非高度元素，而在$ [x，_ny] = 1 $时，有$ x \ mapsto y $，仅当$ n \ in。 $ g/z _ {\ infty}（g）$既不是frobenius也不简单。
For a finite group $G,$ we investigate the direct graph $Γ(G),$ whose vertices are the non-hypercentral elements of $G$ and where there is an edge $x\mapsto y$ if and only if $[x,_ny]=1$ for some $n \in \mathbb N.$ We prove that $Γ(G)$ is always weakly connected and is strongly connected if $G/Z_{\infty}(G)$ is neither Frobenius nor almost simple.
