A subgroup A of a finite group G is called a local covering subgroup of G if A^G = AB for all maximal G-invariant subgroup B of A^G = 〈A^g, g ∊ G〉. Let p be a prime and d be a positive integer. Assume that all subgroups of p^d, and all cyclic subgroups of order 4 when p^d = 2 and a Sylow 2-subgroup of G is nonabelian, of G are local covering subgroups. Then G is p-supersolvable whenever p^d = p or \({p^d} \le \sqrt {{{\left| G \right|}_p}} \) or p^d ≤ ∣O_p’p(G)∣_p/p.

中文翻译：

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有限组中的本地覆盖子组

一个分组甲有限群G ^被称为的局部覆盖亚组ģ如果甲^ģ = AB所有最大ģ -invariant亚乙的甲^ģ = <甲^克，克ε ģ >。令p为质数，d为正整数。假设的所有亚组p ^d，以及4阶所有循环子群时p ^d = 2和的西洛2子群G ^是非阿贝尔，的ģ是本地覆盖子组。然后ģ是p -supersolvable每当p ^d = p或\（{P ^ d} \文件\ SQRT {{{\左| G \右|} _p}} \）或p ^d ≤| ø _P'P（ģ）∣ _p / p。