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- W2992306678 abstract "Let k>0 an integer. F, τ, N, N k , and A denote, respectively, the classes of finite, torsion, nilpotent, nilpotent of class at most k, group in which every two generator subgroup is in N k and abelian groups. The main results of this paper is, firstly, to prove that in the class of finitely generated FN-group, the property FC is closed under finite extension. Secondly, we prove that a finitely generated τN-group in the class ((τN k )τ,∞) ( respectively ((τN k )τ,∞) ∗ ) is a τ -group (respectively τN c for certain integer c=c(k) ) and deduce that a finitely generated FN-group in the class ((FN k )F,∞) (respectively ((FN k )F,∞) ∗ ) is -group (respectively FN c for certain integer c=c(k)). Thirdly we prove that a finitely generated NF-group in the class ((FN k )F,∞) ( respectively ((FN k )F,∞) ∗ ) is F-group (respectively N c F for certain integer c=c(k)). Finally and particularly, we deduce that a finitely generated FN-group in the class ((FA)F,∞) (respectively ((FC)F,∞) ∗ , ((FN ₂ )F,∞) ∗ ) is in the class FA (respectively FN ₂ , FN ₃ (2) ) ." @default.
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- W2992306678 date "2018-06-01" @default.
- W2992306678 modified "2023-09-23" @default.
- W2992306678 title "On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FN k -groups" @default.
- W2992306678 hasPublicationYear "2018" @default.
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