@article { author = {Mohammadzadeh, F. and Mohammadzadeh, E.}, title = {On $\alpha$-solvable fundamental groups}, journal = {Journal of Algebraic Hyperstructures and Logical Algebras}, volume = {2}, number = {2}, pages = {35-46}, year = {2021}, publisher = {University of Hatef (Hatef College University)}, issn = {2676-6000}, eissn = {2676-6019}, doi = {10.52547/HATEF.JAHLA.2.2.35}, 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 = {Fuzzy hypergroup,fundamental relation,$alpha$-solvable group}, url = {https://jahla.hatef.ac.ir/article_132755.html}, eprint = {https://jahla.hatef.ac.ir/article_132755_745d49519fe12905cc1c482af9c1f924.pdf} }