A complete classification of weakly Dedekind groups-Reference-Cited by-同舟云学术

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A complete classification of weakly Dedekind groups

Published:2024 Issue:4 Volume:9 Page:7955-7972
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Shi Huaguo¹,Han Zhangjia²,Guo Pengfei³

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference13 articles.

1. D. J. S. Robinson, A course in the theory of groups, Springer-Verlag, New York-Heidelberg-Berlin, 1980. https://doi.org/10.1007/978-1-4419-8594-1

2. G. Pic, Despre structura grupurilor quasihamiltoniene, Buletin Ştiinţific, 1949.

3. J. T. Buckley, J. C. Lennox, J. Wieglod, Generalizations of Hamiltonian groups, Ric. Mat., 41 (1992), 369–376.

4. Z. Bozikov, Z. Janko, A complete classification of finite $p$-groups all of whose noncyclic subgroups are normal, Glas. Mat., 44 (2009), 177–185. https://doi.org/10.3336/gm.44.1.10

5. L. H. Zhang, J. Q. Zhang, Finite $p$-groups all of whose non-normal abelian subgroups are cyclic, J. Algebra Appl., 12 (2013), 1350052. https://doi.org/10.1142/S0219498813500527

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