TY - JOUR ID - 1137 TI - Results on Engel Fuzzy Subgroups JO - Algebraic Structures and Their Applications JA - AS LA - en SN - 2382-9761 AU - Mohamadzadeh, E. AU - Borzouei, R.A. AU - Jun, Young Bae AD - ‎Department of mathematics Payame Noor University P.O‎. ‎Box 19395-3697 Tehran‎, ‎Iran. AD - Department of mathematics Shahid Beheshti University‎, ‎G‎. ‎C.‎, ‎ Tehran‎, ‎Iran. AD - Department of Mathematics Education, Gyeong sang National university, Chinju, Korea Y1 - 2017 PY - 2017 VL - 4 IS - 2 SP - 1 EP - 14 KW - n-Engel group‎ KW - ‎(torsion free) n-Engle fuzzy subgroup‎ KW - ‎generalized nilpotent fuzzy subgroup DO - 10.22034/as.2017.1137 N2 - ‎In the classical group theory there is‎ an open question‎: ‎Is every torsion free n-Engel group (for n ≥ 4)‎, nilpotent?‎. ‎To answer the question‎, ‎Traustason‎ [11] showed that with some additional conditions all‎ ‎4-Engel groups are locally nilpotent‎. ‎Here‎, ‎we gave some partial‎ answer to this question on Engel fuzzy subgroups‎. ‎We show that if μ is a normal 4-Engel fuzzy‎ subgroup of group G‎, ‎x,y in G and a =yx‎, ‎then μ|< a‎, ‎y‎‎> is a generalized nilpotent of class at‎ most 2‎. ‎Also we define a torsion free fuzzy subgroup and show‎ ‎that if μ is a 4-Engel torsion free fuzzy subgroup of G‎, ‎then μ|< a‎, ‎y‎‎> is a generalized nilpotent of class at most 4‎, ‎for conjugate elements a,y in G‎.  UR - https://as.yazd.ac.ir/article_1137.html L1 - https://as.yazd.ac.ir/article_1137_f2037c3d0ac22a236d52bb0d8f93c479.pdf ER -