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

Mourad Chelgham; Mohamed Kerada; Lemnouar Noui

EN

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

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_cF 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⁾).

Keywords

FC-group,(FC)F-group,(τNk)τ-group,(FNk)F-group,((FNk)F,∞)-group,∞)∗-group,finitely generated group

References

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Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Mourad Chelgham This is me

Mohamed Kerada This is me

Lemnouar Noui This is me

Publication Date

June 1, 2018

Submission Date

March 11, 2018

Acceptance Date

-

Published in Issue

Year 2018 Number: 23

IZ

https://izlik.org/JA24JM99RB

APA

Chelgham, M., Kerada, M., & Noui, L. (2018). On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FNk-groups. Journal of New Theory, 23, 22-30. https://izlik.org/JA24JM99RB

AMA

1.Chelgham M, Kerada M, Noui L. On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FNk-groups. JNT. 2018;(23):22-30. https://izlik.org/JA24JM99RB

Chicago

Chelgham, Mourad, Mohamed Kerada, and Lemnouar Noui. 2018. “On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FNk-Groups”. Journal of New Theory, nos. 23: 22-30. https://izlik.org/JA24JM99RB.

EndNote

Chelgham M, Kerada M, Noui L (June 1, 2018) On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FNk-groups. Journal of New Theory 23 22–30.

IEEE

[1]M. Chelgham, M. Kerada, and L. Noui, “On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FNk-groups”, JNT, no. 23, pp. 22–30, June 2018, [Online]. Available: https://izlik.org/JA24JM99RB

ISNAD

Chelgham, Mourad - Kerada, Mohamed - Noui, Lemnouar. “On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FNk-Groups”. Journal of New Theory. 23 (June 1, 2018): 22-30. https://izlik.org/JA24JM99RB.

JAMA

1.Chelgham M, Kerada M, Noui L. On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FNk-groups. JNT. 2018;:22–30.

MLA

Chelgham, Mourad, et al. “On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FNk-Groups”. Journal of New Theory, no. 23, June 2018, pp. 22-30, https://izlik.org/JA24JM99RB.

Vancouver

1.Mourad Chelgham, Mohamed Kerada, Lemnouar Noui. On Finite Extension and Conditions on Infinite Subsets of Finitely Generated FC and FNk-groups. JNT [Internet]. 2018 Jun. 1;(23):22-30. Available from: https://izlik.org/JA24JM99RB