Finite p-groups in which the number of subgroups of possible order is less than or equal to p ³

Abstract

In this paper, groups of order p ⁿ in which the number of subgroups of possible order is less than or equal to p ³ are classified. It turns out that if p > 2, n ≥ 5, then the classification of groups of order p ⁿ in which the number of subgroups of possible order is less than or equal to p ³ and the classification of groups of order p ⁿ with a cyclic subgroup of index p ² are the same.

Keywords

Inner abelian p-groups / Metacyclic p-groups / Groups of order p ⁿ with a cyclic subgroup of index p ² / The number of subgroups

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