论文标题
有限群体的溶解性和努力的标准
Criteria for solubility and nilpotency of finite groups with automorphisms
论文作者
论文摘要
让$ g $是一个有限的集团，承认企业自动形态$α$。令$ j_g（α）$表示所有换向器$ [x，α] $的集合，其中$ x $属于$ g $的$α$ invariant sylow子组。我们表明$ [g，α] $是且仅当来自集合$ j_g（α）$的一对coprime订单生成的任何子组时，才能溶于或nilpotent。
Let $G$ be a finite group admitting a coprime automorphism $α$. Let $J_G(α)$ denote the set of all commutators $[x,α]$, where $x$ belongs to an $α$-invariant Sylow subgroup of $G$. We show that $[G,α]$ is soluble or nilpotent if and only if any subgroup generated by a pair of elements of coprime orders from the set $J_G(α)$ is soluble or nilpotent, respectively.
