In this paper, groups of order pn in which the number of subgroups of possible order is less than or equal to p3 are classified. It turns out that if p > 2, n ≥ 5, then the classification of groups of order pn in ...In this paper, groups of order pn in which the number of subgroups of possible order is less than or equal to p3 are classified. It turns out that if p > 2, n ≥ 5, then the classification of groups of order pn in which the number of subgroups of possible order is less than or equal to p3 and the classification of groups of order pn with a cyclic subgroup of index p2 are the same.展开更多
基金supported by the National Natural Science Foundation of China(No.10671114)the ShanxiProvincial Natural Science Foundation of China(No.2008012001)the Returned Abroad-StudentFund of Shanxi Province(No.[2007]13-56)
文摘In this paper, groups of order pn in which the number of subgroups of possible order is less than or equal to p3 are classified. It turns out that if p > 2, n ≥ 5, then the classification of groups of order pn in which the number of subgroups of possible order is less than or equal to p3 and the classification of groups of order pn with a cyclic subgroup of index p2 are the same.