In this paper, the notion of the normal level sub HX group is introduced. We discuss the properties of normal level sub HX groups of a bipolar fuzzy normal HX subgroup of a HX group under homomorphism and anti-homomorphism. AMS Subject Classification (2000): 20N25, 03E72, 03F055, 06F35, 03G25. Keywordsfuzzy set, bipolar fuzzy set, bipolar fuzzy HX subgroup, bipolar fuzzy normal HX subgroup, lev...

a subgroup $h$ is said to be $nc$-supplemented in a group $g$ if there exists a subgroup $kleq g$ such that $hklhd g$ and $hcap k$ is contained in $h_{g}$, the core of $h$ in $g$. we characterize the supersolubility of finite groups $g$ with that every maximal subgroup of the sylow subgroups is $nc$-supplemented in $g$.

‎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 ...

The definition of a D-admissible fuzzy subset for an operator domain D on a group G is modified to obtain new kinds of (∈,∈ ∨q)-fuzzy subgroups such as an (∈,∈ ∨q)-fuzzy normal subgroup, an (∈,∈ ∨q)-fuzzy characteristic subgroup, an (∈,∈ ∨q)fuzzy fully invariant subgroup which are invariant under D. As results, some of the fundamental properties of such (∈,∈ ∨q)−fuzzy subgroups are obtained.

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

in this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. furthermore,...

To each fuzzy subgroup a fuzzy equivalence relation is associated and it is proved that a fuzzy subgroup is normal if and only if the operation of the group is compatible with its associated fuzzy equivalence relation. In the de-nition of fuzzy subgroup only the subset is fuzzy whilst the group operation remains crisp. In an opposite direction, another structure can be constructed maintaining c...

in this paper, we study the notion of solvable $l$-subgroup of an $l$-group and provide its level subset characterization and this justifies the suitability of this extension. throughout this work, we have used normality of an $l$-subgroup of an $l$-group in the sense of wu rather than liu.

ABSTRACT In this article an attempt has been made to study some new algebraic structures of intuitionistic multi-anti fuzzy normal subgroups under homomorphism are discussed. Keywords Intuitionistic multi-fuzzy set (IMFS), subgroup (IMAFSG), (IMAFNSG). Mathematics Subject Classification 20N25, 03E72, 08A72, 03F55, 06F35, 03G25, 08A05

In this paper, the notions of   , q  -Q-fuzzy subgroup and normal subgroup are introduced and some of their properties are investigated.