摘要
A subgroup of index p^k of a finite p-group G is called a k-maximal subgroup of G.Denote by d(G) the number of elements in a minimal generator-system of G and by δ_k(G) the number of k-maximal subgroups which do not contain the Frattini subgroup of G.In this paper,the authors classify the finite p-groups with δ_(d(G))(G) ≤ p^2 and δ_(d(G)-1)(G) = 0,respectively.
A subgroup of index pk of a finite p-group G is called a k-maximal subgroup of G. Denote by d（G） the number of elements in a minimal generator-system of G and by δk （G） the number of k-maximal subgroups which do not contain the Frattini subgroup of G. In this paper, the authors classify the finite p-groups with δd（G）（G） ≤ p2 and δd（G）-1 （G） = 0, respectively.
基金
supported by the National Natural Science Foundation of China(Nos.11371232,11371177)
