A complete classification of weakly Dedekind groups

Huaguo Shi; Zhangjia Han; Pengfei Guo; Huaguo Shi; Zhangjia Han; Pengfei Guo

doi:10.3934/math.2024387

AIMS Mathematics

2024, Volume 9, Issue 4: 7955-7972. doi: 10.3934/math.2024387

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Research article Special Issues

A complete classification of weakly Dedekind groups

1.
Department of Teacher Education, Sichuan Vocational and Technical College, Suining 629000, China
2.
School of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China
3.
School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China

Received: 30 November 2023 Revised: 31 January 2024 Accepted: 07 February 2024 Published: 26 February 2024
MSC : 20D35, 20E34

A finite group is called a weakly Dedekind group if all its noncyclic subgroups are normal. In this paper, we determine the complete classification of weakly Dedekind groups.
- finite group,
- normal subgroup,
- cyclic subgroup,
- $ p $-group
Citation: Huaguo Shi, Zhangjia Han, Pengfei Guo. A complete classification of weakly Dedekind groups[J]. AIMS Mathematics, 2024, 9(4): 7955-7972. doi: 10.3934/math.2024387

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Abstract

A finite group is called a weakly Dedekind group if all its noncyclic subgroups are normal. In this paper, we determine the complete classification of weakly Dedekind groups.

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