论文标题
满足独立财产的有限团体
Finite groups satisfying the independence property
论文作者
论文摘要
我们说，如果每对不同的元素$ x $和$ y $的$ g $，则满足独立性的$ g $，则$ \ {x，y \} $都包含在$ g $的最小生成集中，或一个$ x $，而$ x $，而$ y $是其他功能。我们将有限组的完整分类与此属性进行了分类，尤其是证明每个这样的组都是超溶的。我们证明的关键要素是一个定理，表明除三个有限的几乎简单的组$ h $以外的所有元素都包含一个元素$ s $，因此最大的亚组包含$ s $，但不包含$ h $的socle，均为成对的非偶联物。
We say that a finite group $G$ satisfies the independence property if, for every pair of distinct elements $x$ and $y$ of $G$, either $\{x,y\}$ is contained in a minimal generating set for $G$ or one of $x$ and $y$ is a power of the other. We give a complete classification of the finite groups with this property, and in particular prove that every such group is supersoluble. A key ingredient of our proof is a theorem showing that all but three finite almost simple groups $H$ contain an element $s$ such that the maximal subgroups of $H$ containing $s$, but not containing the socle of $H$, are pairwise non-conjugate.
