论文标题
亚标准级和有限组中的可溶性
Subnormalizers and solvability in finite groups
论文作者
论文摘要
对于有限的$ g $，我们研究概率$ sp（g）$，鉴于两个元素$ x，y \ in g $，环状子组$ \ langle x \ rangle $在子组$ \ langle x，y \ rangle $中是亚正常。这可以看作是两个元素生成nilpotent子组的概率与两个元素生成可解决的子组的概率之间的中间不变的。我们证明，每个不可用的$ g $ $ sp（g）\ leq 1/6 $。
For a finite group $G$, we study the probability $sp(G)$ that, given two elements $x,y \in G$, the cyclic subgroup $\langle x \rangle$ is subnormal in the subgroup $\langle x, y \rangle$. This can be seen as an intermediate invariant between the probability that two elements generate a nilpotent subgroup and the probability that two elements generate a solvable subgroup. We prove that $sp(G) \leq 1/6$ for every nonsolvable group $G$.
