Galoitica: Journal of Mathematical Structures and Applications

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Galoitica: Journal of Mathematical Structures and Applications

Volume 1 , Issue 1 , PP: 12-35, 2022 | Cite this article as | XML | Html | PDF

On A Novel Group Derived From a Generalization of Integer Exponents and Open Problems

Oliver V. Shtawzen 1 *

  • 1 University Of Nizwa, Sultanate Of Oman - (Vonshtawzen1970abc@gmail.com)
  • Doi: https://doi.org/10.54216/GJMSA.010102

    Received: March 12, 2022 Accepted: May 03, 2022
    Abstract

     This paper is devoted to defining a new generalization of m-power closed groups by using some special mappings defined on a group (power maps). Also, a new group will be presented according to these mappings which will be related to other algebraic structures.

    Keywords :

    Power map , m-power closed group , integer exponent , MA-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). 

    [2] Levi, F. Notes on Group Theory, J. Indian Math. Soc. 8, (1944), pp.1-7.

    [3] Kappe, L. and Ying, Y. On Exact Power Margin Groups, Rend. Sem. Mat. University of Padova. Vol. 87, (1992), pp.245-265.

    [4]  Haushi, M. The Algebraic Structures 1, Tishreen University Press, (2004).

    [5] Rotman, Joseph J. An introduction to the theory of groups. Fourth edition. Graduate Texts in Mathematics, 148. Springer-Verlag, New York, 1995.

    [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.

     

     

    Cite This Article As :
    Oliver V. Shtawzen. "On A Novel Group Derived From a Generalization of Integer Exponents and Open Problems." Full Length Article, Vol. 1, No. 1, 2022 ,PP. 12-35 (Doi   :  https://doi.org/10.54216/GJMSA.010102)
    Oliver V. Shtawzen. (2022). On A Novel Group Derived From a Generalization of Integer Exponents and Open Problems. Journal of , 1 ( 1 ), 12-35 (Doi   :  https://doi.org/10.54216/GJMSA.010102)
    Oliver V. Shtawzen. "On A Novel Group Derived From a Generalization of Integer Exponents and Open Problems." Journal of , 1 no. 1 (2022): 12-35 (Doi   :  https://doi.org/10.54216/GJMSA.010102)
    Oliver V. Shtawzen. (2022). On A Novel Group Derived From a Generalization of Integer Exponents and Open Problems. Journal of , 1 ( 1 ), 12-35 (Doi   :  https://doi.org/10.54216/GJMSA.010102)
    Oliver V. Shtawzen. On A Novel Group Derived From a Generalization of Integer Exponents and Open Problems. Journal of , (2022); 1 ( 1 ): 12-35 (Doi   :  https://doi.org/10.54216/GJMSA.010102)
    Oliver V. Shtawzen, On A Novel Group Derived From a Generalization of Integer Exponents and Open Problems, Journal of , Vol. 1 , No. 1 , (2022) : 12-35 (Doi   :  https://doi.org/10.54216/GJMSA.010102)