Finite p-groups with few non-major k-maximal subgroups

Abstract

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.

Keywords

Finite p-groups / k-Maximal subgroups / k-Major subgroups / Frattini subgroup / The number of non-major k-maximal subgroups

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