# 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