论文标题
关于$ LC $ -NILPOTENT组的结构
On the structure of $LC$-nilpotent groups
论文作者
论文摘要
对于有限的组$ g $，让$ lc（g）$是元素$ x $生成的子组，以使所有$ y \ in g $ in g $和所有整数$ n $，$ x^n y $的订单划分为$ x $和y $的最低订单的订单。该亚组是$ g $的尼尔植物特征子组。在本文中，除其他结果外，我们还表明，当$ g $不包含任何$ 2 $ -FROBENIUS子类$（P，Q，Q，P）$时，有限的可解决组$ G $在$ LC $ -NILPOTENT系列中接受。由于该定理的结果，我们得出结论，包括所有$ lc $ nilpotent群体组成的代数系统形成了多种多样。
For a finite group $G$, let $LC(G)$ be the subgroup generated by elements $x$ such that, for all $y \in G$ and all integers $n$, the order of $x^n y$ divides the least common multiple of the orders of $x$ and $y$. This subgroup is a nilpotent characteristic subgroup of $G$. In this article, among other results, we show that a finite solvable group $G$ admits an $LC$-nilpotent series if and only if $G$ does not contain any $2$-Frobenius subgroup of type $(p, q, p)$. As a consequence of this theorem, we conclude that the algebraic system comprising all $LC$-nilpotent groups forms a variety.
