In this paper, we study the inter-connections of the notions of commutator L-subgroups, nilpotent L-subgroups, conjugate L-subgroups and normalizer of L-subgroups like their classical counterparts. Throughout the development of this paper, the parent group is an L-group rather than an ordinary group. Our main result in this work is that every nilpotent L-subgroup of an L-group satisfies the normalizer condition.
Abu OsmanM.T., On some product of fuzzy subgroups, Fuzzy Sets and Systems24 (1987), 79–86.
2.
AjmalN., Set product and fuzzy subgroups, in Proc of IFSA World Congress, Belgium, 1991, 3–7.
3.
AjmalN., The lattice of fuzzy normal subgroups is modular, Inform Sci83 (1995), 199–209.
4.
AjmalN., Fuzzy groups with sup property, Inform. Sci93 (1996), 247–264.
5.
AjmalN., Homomorphism of fuzzy groups, correspondence theorem and fuzzy quotient groups, Fuzzy Sets and Systems61 (1994), 329–339.
6.
AjmalN., Fuzzy group theory: A comparison of different notions of product of fuzzy sets, Fuzzy Sets and Systems110 (2000), 437–446.
7.
AjmalN. and ThomasK.V., A new blueprint for fuzzification: An application to lattices of fuzzy congruences, The Journal of Fuzzy Mathematics7 (1999), 499–512.
8.
AjmalN. and ThomasK.V., The lattices of fuzzy subgroups and fuzzy normal subgroups, Inform Sci76 (1994), 1–11.
9.
AjmalN. and ThomasK.V., A complete study of the lattices of fuzzy congruences and fuzzy normal subgroups, Inform Sci82 (1995), 197–218.
10.
AjmalN. and JahanI., Normal Closure of an L-subgroup of an L-group, The Journal of Fuzzy Mathematics22 (2014), 115–126.
11.
AjmalN. and JahanI., Nilpotency and theory of L subgroups of an L-group, Fuzzy Information and Engineering6 (2014), 1–17.
12.
AjmalN. and JahanI., An L-point characterization of normality and normalizer of an L-subgroup of anL-group, Fuzzy Information and Engineering6 (2014), 147–166.
13.
AjmalN. and JahanI., Solvable L-subgroup of an L-group, Iranian Journal of Fuzzy Systems12 (2015), 151–161.
14.
AjmalN. and JahanI., Generated L-subgroup of an L-group, Iranian Journal of Fuzzy Systems12 (2015), 129–136.
15.
AjmalN. and ThomasK.V., A complete study of the lattices of fuzzy congruences and fuzzy normal subgroups, Inform Sci82 (1995), 197–218.
16.
AkgulM., Some properties of fuzzy subgroups, J Math Anal Appl133 (1988), 93–100.
17.
AkramM., Intuitionistic, (S; T)-fuzzy Lie ideals of Lie algebras, Quasigroups and Related Systems15 (2007), 201–218.
18.
AkramM. and FarooqeA., m-polar fuzzy Lie ideals of Lie algebras, Quasigroups and Related Systems24 (2016), 141–150.
19.
AlkhameesY., Fuzzy direct product of fuzzy subgroups of subgroups, Journal of Fuzzy Mathematics1 (1998), 1–12.
20.
AnthonyJ.M. and SherwoodH., A characterisation of fuzzy subgroups, Fuzzy Sets and Systems7 (1982), 297–305.
21.
AsaadM. and ZaidS.A., A contribution to the theory of fuzzy subgroups, Fuzzy Sets and Systems77 (1996), 355–369.
22.
BhakatS.K. and DasP., On the definition of fuzzy subgroups, Fuzzy Sets and Systems51 (1992), 235–241.
23.
BhattacharyaP. and MukherjeeN.P., Fuzzy groups: Some group theoretic analogs II, Inform Sci41 (1987), 77–91.
24.
ChenD.G. and GuW.X., Product structure of fuzzy factor groups, Fuzzy Sets and Systems60 (1993), 229–232.
25.
DasP.S., Fuzzy groups and level subgroups, J Math Anal Appl84 (1981), 264–269.
26.
DixitV.N., KumarR. and AjmalN., Level subgroups and union of fuzzy subgroups, Fuzzy Sets and Systems37 (1990), 359–371.
27.
ErogluM.S., The homomorphic image of a fuzzy subgroup is always a fuzzy subgroup, Fuzzy Sets and Systems33 (1989), 255–256.
28.
FarooqA., AliG. and AkramM., On m-Polar fuzzy groups, International Journal of Algebra and Statistics2 (2016), 115–127.
29.
FelipL., Structure and construction of fuzzy subgroups os a group, Fuzzy Sets and Systems51 (1992), 105–109.
30.
FosterD.H., Fuzzy topological groups, J Math Anal Appl67 (1979), 549–564.
31.
GoguenJ.A., L-fuzzy sets, J Math Anal Appl18 (1967), 145–174.
32.
JahanI., DavvazB. and AjmalN., Nilpotent, L-subgroups and the set product of L-subsets, European Journal of Pure and Applied Mathematics10 (2017), 255–271.
33.
GuptaK.C. and SarmaB.K., Nilpotent fuzzy groups, Fuzzy Sets and Systems101 (1999), 167–176.
34.
HeadT., A metatheorem for deriving fuzzy theorems from crisp versions, Fuzzy Sets and Systems73 (1995), 349–358.
RosenfeldA., Fuzzy groups, J Math Anal Appl35 (1971), 512–517.
45.
SaxenaP.K., Fuzzy subgroups as union of two fuzzy subgroups, Fuzzy Sets and Systems57 (1993), 209–218.
46.
SultanaN. and AjmalN., Generated fuzzy subgroups: A modification, Fuzzy Sets and Systems107 (1999), 241–243.
47.
WuW., Normal fuzzy subgroups, Fuzzy Math1 (1981), 21–30.
48.
YuY., MordesonJ.N. and ChengS.C., Elements of algebra, Lecture Notes in Fuzzy Mathematics and Computer Science, Center for Research in Fuzzy Mathematics and Computer Science, Creighton University, USA, 1994.
49.
YuY., A theory of isomorphism of fuzzy groups, Fuzzy Systems and Math2 (1988), 57–68.
50.
ZhanJ., LiuQ. and HerawanT., A novel soft rough set: Soft rough hemirings and its multicriteria group decision making, Applied Soft Computing54 (2017), 393–402.
51.
ZhanJ. and ZhuK., A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making, Soft Computing21 (2017), 1923–1936.
52.
ZhanJ., MuhammadI. and AliN., Mehmood, On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods, Applied Soft Computing56 (2017), 446–457.
53.
PanW. and ZhanJ., Rough fuzzy groups and rough soft groups, Italian Journal of Pure and Applied Mathematics36 (2016), 617–628.
