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,∞)^{∗},
((FN₂)F,∞)^{∗})
is in the class FA (respectively FN₂,
FN₃^{(2)}).
Primary Language | en |
---|---|
Journal Section | Research Article |
Authors | |
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. |