Frattini submultigroups of multigroups

Joseph Achile Otuwe, Musa Adeku Ibrahim

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.


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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.




DOI: http://dx.doi.org/10.23755/rm.v39i0.534

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