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Research Article | Open Access

A complete classification of weakly Dedekind groups

Huaguo Shi1, Zhangjia Han2, Pengfei Guo3( )
Department of Teacher Education, Sichuan Vocational and Technical College, Suining 629000, China
School of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China
School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China
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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.

Keywords

finite groupnormal subgroupcyclic subgroupp-group
CLC number: 20D35, 20E34

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AIMS Mathematics
Volume 9 Issue 4,
April 2024
Pages 7955-7972
DOI: 10.3934/math.2024387

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Shi H, Han Z, Guo P. A complete classification of weakly Dedekind groups. AIMS Mathematics, 2024, 9(4): 7955-7972. https://doi.org/10.3934/math.2024387

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Received: 30 November 2023
Revised: 31 January 2024
Accepted: 07 February 2024
Published: 15 April 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)