Year 2018, Volume , Issue 23, Pages 22 - 30 2018-06-01

On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FNk-groups

Mourad CHELGHAM [1] , Mohamed KERADA [2] , Lemnouar NOUİ [3]


Let k>0 an integer. F, τ, N, Nk, 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 Nk 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 ((τNk)τ,∞) ( respectively ((τNk)τ,∞)) is a τ-group (respectively τNc for certain integer c=c(k) ) and deduce that a finitely generated FN-group in the class ((FNk)F,∞) (respectively ((FNk)F,∞)) is -group (respectively FNc for certain integer c=c(k)). Thirdly we prove that a finitely generated NF-group in the class ((FNk)F,∞) ( respectively ((FNk)F,∞)) is F-group (respectively NcF 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)F,∞)) is in the class FA (respectively FN, FN(2)).

FC-group, (FC)F-group, (τNk)τ-group, (FNk)F-group, ((FNk)F, ∞)-group, ∞)∗-group, finitely generated group
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Primary Language en
Journal Section Research Article
Authors

Author: Mourad CHELGHAM

Author: Mohamed KERADA

Author: Lemnouar NOUİ

Dates

Publication Date : June 1, 2018

Bibtex @research article { jnt431047, journal = {Journal of New Theory}, issn = {2149-1402}, eissn = {2149-1402}, address = {Mathematics Department, Gaziosmanpasa University 60250 Tokat-TURKEY.}, publisher = {Gaziosmanpasa University}, year = {2018}, volume = {}, pages = {22 - 30}, doi = {}, title = {On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FN<sub>k</sub>-groups}, key = {cite}, author = {CHELGHAM, Mourad and KERADA, Mohamed and NOUİ, Lemnouar} }
APA CHELGHAM, M , KERADA, M , NOUİ, L . (2018). On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FN<sub>k</sub>-groups. Journal of New Theory , (23) , 22-30 . Retrieved from https://dergipark.org.tr/en/pub/jnt/issue/37237/431047
MLA CHELGHAM, M , KERADA, M , NOUİ, L . "On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FN<sub>k</sub>-groups". Journal of New Theory (2018 ): 22-30 <https://dergipark.org.tr/en/pub/jnt/issue/37237/431047>
Chicago CHELGHAM, M , KERADA, M , NOUİ, L . "On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FN<sub>k</sub>-groups". Journal of New Theory (2018 ): 22-30
RIS TY - JOUR T1 - On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FN<sub>k</sub>-groups AU - Mourad CHELGHAM , Mohamed KERADA , Lemnouar NOUİ Y1 - 2018 PY - 2018 N1 - DO - T2 - Journal of New Theory JF - Journal JO - JOR SP - 22 EP - 30 VL - IS - 23 SN - 2149-1402-2149-1402 M3 - UR - Y2 - 2020 ER -
EndNote %0 Journal of New Theory On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FN<sub>k</sub>-groups %A Mourad CHELGHAM , Mohamed KERADA , Lemnouar NOUİ %T On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FN<sub>k</sub>-groups %D 2018 %J Journal of New Theory %P 2149-1402-2149-1402 %V %N 23 %R %U
ISNAD CHELGHAM, Mourad , KERADA, Mohamed , NOUİ, Lemnouar . "On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FN<sub>k</sub>-groups". Journal of New Theory / 23 (June 2018): 22-30 .
AMA CHELGHAM M , KERADA M , NOUİ L . On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FN<sub>k</sub>-groups. JNT. 2018; (23): 22-30.
Vancouver CHELGHAM M , KERADA M , NOUİ L . On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FN<sub>k</sub>-groups. Journal of New Theory. 2018; (23): 30-22.