1
University Of Nizwa, Sultanate Of Oman
(Vonshtawzen1970abc@gmail.com)
Abstract :
The generalizations of abelian groups have been studied widely because of their importance in classification theorem and representation. A group G is called an m-power closed group or (m-group) if and only if it has the following property xm ym=zm ∀x,y ∈ G and for z ∈ G. This paper studies a special case of m-groups, when G is a finite m-group and n-group at the same time with relatively prime integers m and n, which is called a Monic group. It presents the necessary and sufficient conditions for a monic group G to be cyclic, abelian, nilpotent, and solvable by the corresponding property of its power subgroups Gm , Gn. Also, this work introduces three open problems in the theory of finite groups.
Keywords :
m-power closed group; m-abelian group; monic group.
References :
[1] Abobala, M. and Sankari, H. A Contribution to (m-Power Closed) Groups, UMM Al-Qura University Journal of Applied Science (UQUJAS), KSA, (2020).
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[6] Arad, Z. and Ward, M. New Criteria for the Solvability of Finite Groups, Journal of Algebra, 77, (1982), pp. 234-246.
[7] Dolfi, S. Guralnik, R. Herzog, M. and Praeger, C. A New Solvability Criterion for Finite Groups, ArXiv:1007.5394, (2011).
[8] Sankari, H., and Abobala, M., On A New Criteria For the Solvability of Non-Simple Finite Groups and m-Abelian Solvability, Journal of Mathematics, Hindawi, 2021.
[9] Hatip, A., Alhamido, R., and Abobala, M., "A Contribution to Neutrosophic Groups", International Journal of Neutrosophic Science", Vol. 0, pp. 67-76 . 2019.
[10] Abobala, M., " n-Refined Neutrosophic Groups I", International Journal of Neutrosophic Science, Vol. 0, pp. 27-34. 2020.
| Style | # |
|---|---|
| MLA | Oliver V. Shtawzen. "On Some Applications and Open Problems about (m-Groups)." Galoitica: Journal of Mathematical Structures and Applications, Vol. 1, No. 1, 2022 ,PP. 48-51 (Doi : https://doi.org/10.54216/GJMSA.010105) |
| APA | Oliver V. Shtawzen. (2022). On Some Applications and Open Problems about (m-Groups). Journal of Galoitica: Journal of Mathematical Structures and Applications, 1 ( 1 ), 48-51 (Doi : https://doi.org/10.54216/GJMSA.010105) |
| Chicago | Oliver V. Shtawzen. "On Some Applications and Open Problems about (m-Groups)." Journal of Galoitica: Journal of Mathematical Structures and Applications, 1 no. 1 (2022): 48-51 (Doi : https://doi.org/10.54216/GJMSA.010105) |
| Harvard | Oliver V. Shtawzen. (2022). On Some Applications and Open Problems about (m-Groups). Journal of Galoitica: Journal of Mathematical Structures and Applications, 1 ( 1 ), 48-51 (Doi : https://doi.org/10.54216/GJMSA.010105) |
| Vancouver | Oliver V. Shtawzen. On Some Applications and Open Problems about (m-Groups). Journal of Galoitica: Journal of Mathematical Structures and Applications, (2022); 1 ( 1 ): 48-51 (Doi : https://doi.org/10.54216/GJMSA.010105) |
| IEEE | Oliver V. Shtawzen, On Some Applications and Open Problems about (m-Groups), Journal of Galoitica: Journal of Mathematical Structures and Applications, Vol. 1 , No. 1 , (2022) : 48-51 (Doi : https://doi.org/10.54216/GJMSA.010105) |