On minimal non-(Hypercentral-By-Cernikov) Groups

Authors

  • Bouchelaghem Mounia Laboratory of Fundamental and Numerical Mathematics, Departments of Mathematics, University Setif 1, 19000 Setif, Algeria
  • Azra Souad Department of Mathematics, Faculty of Mathematics and Computer Science, University Mohamed El-Bachir El-Ibrahimi of Bordj BouArreridj, Bordj BouArreridj, 34030 El AnasserBordj,BouArreridj, Algeria
  • Benkrima Yamina Ecole Normale Superieure de Ouargla, 30000 Ouargla, Algeria

Keywords:

Hypercentral, Cernikov, Hypercentral-by-Cernikov, Minimal non- Ω

Abstract

If X is a class of groups, then a group is said to be minimal non-X if it is not an X-group, while all its proper subgroups belong to X. The main result of this note is if G is a minimal non-ZAC group , then G is a finitely generated perfect group which has no proper subgroup of finite index and such that G/Frat(G) is an infinite simple group, where ZA ( respectively, C) denotes the class of hypercentral groups, (respectively,  the class of Cernikov groups), and Frat(G) stands for the Frattini subgroup of G.

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Published

2024-08-24

How to Cite

Bouchelaghem Mounia, Azra Souad, & Benkrima Yamina. (2024). On minimal non-(Hypercentral-By-Cernikov) Groups. Journal of Computational Analysis and Applications (JoCAAA), 33(06), 427–429. Retrieved from http://eudoxuspress.com/index.php/pub/article/view/799

Issue

Vol. 33 No. 06 (2024): JOCAAA

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.