On $\alpha$-solvable fundamental groups

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Science, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

2 Department of Mathematics, Faculty of Science, Payame Noor University, Tehran, Iran

Abstract

We introduce a specific kind of equivalence relation ${\xi^*}_n^{\alpha}$ on a fuzzy hypergroup S such that the quotient $S/ {\xi^*}_n^{\alpha}$, the set of all equivalence classes, is an $\alpha$-solvable group. This helps us to introduce the $\alpha$-solvable fundamental relation $\xi^{*\alpha}$. In particular, we obtain an equivalent condition with transitivity of $\xi^\alpha$.

Keywords

References

[1] R. Ameri, T. Nozari, Complete parts and fundamental relation on fuzzy hypersemigroups,
Journal of Multiple-Valued Logic and Soft Computing, 19 (2011), 451{460.
[2] R. Barzegar, A. Erfanian, Nilpotency and solubility of groups relative to an automorphism,
Caspian Journal of Mathematical Sciences, 4(2) (2015), 271{283.
[3] R.A. Borzooei, E. Mohammadzadeh, V. Fotea, On Engel fuzzy subpolygroups, New Mathe-
matics and Natural Computation, 13(2) (2017), 165{206.
[4] P. Corsini , Prolegomena of hypergroup theory, Aviani Editore, Tricesimo, 1993.
[5] P. Corsini, I. Tofan, On fuzzy hypergroups, Pure Mathematics and Applications, 8 (1997),
29{37.
[6] D, Freni, A new charactrization of the drived hypergroup via strungly regular equivalences,
Communications in Algebra, 30(8) (2002), 3977{3989.
[7] V. Leoreanu-Fotea, B. Davvaz, Fuzzy hyperrings, Fuzzy Sets and Systems 160(2009), 2366{
2378.
[8] E. Mohammadzadeh, R.A. Borzooei, Y.B. Jun, Results on Engel fuzzy subgroup, Algebraic
Structures and their Applications, 4(2) (2017), 1{14.
[9] E. Mohammadzadeh, R.A. Borzooei, Nilpotent fuzzy subgroups, Mathematics, 6(27) (2018),
1{12.
[10] J.N. Mordeson, M.S. Malik, Fuzzy commutative algebra, Journal of Fuzzy Mathematics, 3
(1995), 1{15.
[11] T. Nozari, Commutative fundamental relation in fuzzy hypersemigroups, Italian Journal of
Pure and Applied Mathematics, 36 (2016), 455{464.
[12] A. Rosenfeld, Fuzzy groups, Journal of Mathematical Analysis and Applications, 35 (1971),
512{517.
[13] M.K. Sen, R. Ameri, G. Chowdhury, Fuzzy hypersemigroups, Soft Computing, 12 (2008),
891{900.
[14] L.A. Zadeh, Fuzzy sets, Information Control, 8 (1965), 338{353.
Journal of Algebraic Hyperstructures and Logical Algebras
Volume 2, Issue 2
May 2021
Pages 35-46

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