Finite p-Groups Whose Number of Subgroups of Each Order Is at most p4

• 来源期刊: 代数集刊（英文版）
• 关键词: finite p-groups enumeration of subgroups type of regular p-groups
• 年，卷（期）: 2019,（3）
• 页码范围: 411-424
• 页数: 14页
• 语种: 英文
• DOI: 10.1142/S1005386719000300

摘要

Assume G is a group of order pn,where p is an odd prime.Let sk(G) denote the number of subgroups of order pk of G.We give a criterion for a p-group to be with sk(G) ≤ p4 for each integer k satisfying 1 ≤ k ≤ n.Moreover,such p-groups are classified.