Frattini submultigroups of multigroups

Authors

  • Joseph Achile Otuwe Department of Mathematics, College of Science, Ahmadu Bello University, Zaria, Nigeria
  • Musa Adeku Ibrahim Department of Mathematics, College of Science, Ahmadu Bello University, Zaria, Nigeria

DOI:

https://doi.org/10.23755/rm.v39i0.534

Abstract

In this paper, we introduce and study maximal submultigroups and present some of its algebraic properties. Frattini submultigroups as an extension of Frattini subgroups is considered. A few submultigroups results on the new concepts in connection to normal, characteristic, commutator, abelian and center of a multigroup are established and the ideas of generating sets, fully and non-fully Frattini multigroups are presented with some significant results.

References

W. Alice. On the Frattini Subgroup, Transactions of the American Mathematical Society, 141, 323-333. 1969.

R. B. J. T. Allenby. Normal Subgroups Contained in Frattini Subgroups are Frattini Subgroups, Proceedings of the American Mathematical Society, 78(3), 315-318. 1980.

M. Aschbacher, and L. Scott. Maximal Subgroup of a Finite Group, Journal of Algebra. 92(1), 44-80. 1985.

J. A. Awolola, and P. A. Ejegwa. On Some Algebraic Properties of Order of an Element of a Multigroup. Quasigroups and Related Systems 25:21-26. 2017.

B. A. Ballester, and L. M. Ezquerro. On Maximal Subgroups of Finite Groups, Comms in Algebra, 19(8), 373-2394. 1991.

J. C. Beidleman and T. K. Seo., Generalized Frattini Subgroups of Finite Groups, Pacific Journal of Mathematics, 23, No. 3, 441-450. 1967.

M. Dresher, and O. Ore. Theory of Multigroups, American J. Math. 60.

P. A. Ejegwa, and A. M. Ibrahim. Normal Submultigroups and Comultisets of a Multigroup, Quasigroups and Related Systems,25: 231-244. 2017a.

P. A. Ejegwa, and A. M. Ibrahim. Some Groups Analogous Results in Multigroup Setting. Annals of Fuzzy Mathematics and Informatics, 17(3): 231-245. 2019.

P. A. Ejegwa, and J. A. Otuwe. Frattini fuzzy subgroups of fuzzy groups. Annals of Communications in Mathematics, 2(1), 24-31. 2019.

F. Giovanni. Intornoalla Generazioni Dei Gruppi di Operazioni, Rend. Accad Lincei 4(1), 281-285. 1885.

A. M. Ibrahim, and P. A. Ejegwa. A Survey on the Concept of Multigroups, Journal of the Nigerian Association of Mathematical Physics, 38: 1-8. 2016.

A. M. Ibrahim, and P. A. Ejegwa. Characteristic Submultigroups of Multigroups, Gulf Journal of Mathematics, 5(4): 1-8. 2017a.

A. M. Ibrahim, and P. A. Ejegwa. Multigroup Actions on Multiset, Annals of Fuzzy Mathematics and Informatics, 14(5): 515-526. 2017b.

C. B. James, and K. S. Tae. Generalized Frattini Subgroups of a Finite Groups, Pacific Journal of Mathematics, 23 (3), 44-450. 1967.

O. Javier. The Frattini Subgroup of a Group, Margarita Mathematica en Memoria de Jose Javier (CHICHO) Guadalupe Hernandes, 1-12. 2001.

G. A. Miller. Maximal Subgroup of a given Group, Proc. N. A. S. Department of Mathematics, University of Illinois, 68-70. 1940.

J. Mohit, and P. Ajit. Nilpotency in Frattini Subgroups, International Journal of Mathematics Trends and Technology, 44, (3),121-122. 2017.

S. K. Nazmul, P. Majumdar, and S. K. Samanta. On Multisets and Multigroups. Annals of Fuzzy Mathematics and Informatics, 6(3): 643-656. 2013.

B. Prabir, and N. P. Mukherjee. A Generalized Frattini Subgroup of a Finite Group, International Journal of Mathematical Science, 12 (2), 263-266. 1989.

A. Stefanos, and B. B. Adolfo. On the Frattini Subgroup of a Finite Group. Journal of Algebra, (16), 1-8. 2016.

D. Singh, A. M. Ibrahim, T. Yohanna and J. N. Singh. An Overview of the Application of Multisets, Novi Sad Journal of Mathematics, 37(2), 73-92. 2007.

A. Syropoulos, Mathematics of Multisets, Springer-verlac Berlin Heidelberg. 2001.

Downloads

Published

2020-12-30

Issue

Vol. 39 (2020)

Section

Volume 39-2020

License

This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. The journal is committed to real and immediate open access for academic work. All of the journal articles are free to access immediately from the date of publication. There are no charge for readers to download articles and reviews for their own scholarly use. Benefits of open access for authors, include:

  • Free access for all users worldwide
  • Increased visibility and readership
  • Rapid publication
  • No spatial constraints
  • Authors can share their research papers on their personal web-pages (i.e. ResearchGate, etc.)

Ratio Mathematica publishes open access articles under the terms of the Creative Commons Attribution (CC BY) License. The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by Ratio Mathematica is retained by the author(s). Authors grant Ratio Mathematica a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified. 
For further information visit: https://creativecommons.org/licenses/by/3.0/. The following logo will appear in any paper that will be published from the volume number 31/2016 onwards.