摘要
Let G be a finite group and H a subgroup of G.The normal index of H in G is defined as the order of K/H_(G),where K is a normal supplement of H in G such that|K|is minimal and H_(G)≤K■G.Let p be a prime which divides the order of a group G.In this paper,some characterizations of G being p-solvable or p-supersolvable were obtained by analyzing the normal index of certain subgroups of G.These results can be viewed as local version of recent results in the literature.
基金
Supported by the National Natural Science Foundation of China(Grant No.12071092)
Guangdong Basic and Applied Basic Research Foundation(Grant No.2025A1515012072)
the Natural Science Research Project of Anhui Educational Committee(Grant No.2024AH051298)
the Scientific Research Foundation of Bozhou University(Grant No.BYKQ202419).
