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- Title
On Finite Extensions of FC-Groups in the Class of NF-Groups.
- Authors
Chelgham, Mourad; Kerada, Mohamed; Noui, Lamnouar; Araci, Serkan
- Abstract
Let F, N, A and N2 denote the properties of being finite, nilpotent, abelian and nilpotent of classes at most 2, respectively. Firstly we consider the class of finitely generated FN-groups. We show that the property FC is closed under finite extensions, and extend this result to finitely generated NF-groups. Secondly we prove that a finitely generated NF-group G is in the class ((FC)F, ∞) if and only if G is an FA-group. Finally we prove that a finitely generated NF-group in the class ((FC)F, ∞)* is an FN2-group. Moreover, G/Z2(G) is finite.
- Subjects
NILPOTENT groups; ABELIAN groups; ISOMORPHISM (Mathematics); POLYNOMIALS; INTEGERS
- Publication
Algebra Colloquium, 2019, Vol 26, Issue 1, p23
- ISSN
1005-3867
- Publication type
Article
- DOI
10.1142/S100538671900004X