摘要
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 Sylow2-subgroup of G is nonabelian,of G are local covering subgroups.Then G is p-supersolvable whenever p^(d)=p or p^(d)≤(√|G|_(p))or p^(d)≤|O_(p'p)(G)|_(p)/p.
基金
Supported by the NSF of China(Grant No.11871011)。
