On Engel Fuzzy Subpolygroups

R. A. Borzooei, E. Mohammadzadeh () and Violeta Fotea ()
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R. A. Borzooei: Department of Mathematics, Shahid Beheshti University, G. C., Tehran, Iran
E. Mohammadzadeh: #x2020;Department of Mathematics, Faculty of Science, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran
Violeta Fotea: #x2021;Faculty of Mathematics, Alexandru Ioan Cuza University, 700506 Iasi, Romania

New Mathematics and Natural Computation (NMNC), 2017, vol. 13, issue 02, 195-206

Abstract: In this paper, by considering the notions of polygroup and Engel group, we introduce the concept of Engel fuzzy subpolygroups. In this regard, by a normal Engel fuzzy subpolygroup μ of P and β*, the fundamental relation on a given polygroup P, we construct an Engel fuzzy subgroup μβ*. We obtain a necessary and sufficient condition between Engel fuzzy subpolygroups and the Engel group P/∼, the group of equivalence classes derived from a fuzzy subpolygroup of P. Finally, by using these results, we get Zorn’s lemma, in the Engel fuzzy subpolygroups.

Keywords: Engel group; Engel polygroup; nilpotent group; fundamental group; fuzzy subpolygroup (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1142/S1793005717500089

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