Groups with few non-(Hypercentral-By-Finite) Subgroups

Authors

  • 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
  • Bouchelaghem Mounia Laboratory of Fundamental and Numerical Mathematics, Departments of Mathematics, University Setif 1, 19000 Setif, Algeria
  • Benkrima Yamina Ecole Normale Superieure de Ouargla, 30000 Ouargla, Algeria

Keywords:

Hypercentral, Finite-by-hypercentral, Hypercentral-by-finite, Minimal non-Ω

Abstract

In this note we study groups with few non-(hyper central-by-finite)subgroups and we prove if G is a minimal non-ZAF group, then G is a finitelygenerated perfect group which has no proper subgroup of finite index and suchthat G/Frat(G) is an infinite simple group, where ZA ( respectively,F) denotesthe class of hypercentral groups, (respectively,the class of Finite groups), andFrat(G) stands for the Frattini subgroup of G.Moreover, we proved a infinitely generated F-perfect MNZAF-group. Gis MNZA-group if, and only if, G is MNFZA-group if, and only if, G is MNZAF

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Published

2024-09-24

How to Cite

Azra Souad, Bouchelaghem Mounia, & Benkrima Yamina. (2024). Groups with few non-(Hypercentral-By-Finite) Subgroups. Journal of Computational Analysis and Applications (JoCAAA), 33(06), 97–100. Retrieved from https://eudoxuspress.com/index.php/pub/article/view/710

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.