Let $H$, $L$ and $X$ be subgroups of a finite group$G$. Then $H$ is said to be $X$-permutable with $L$ if for some$xin X$ we have $AL^{x}=L^{x}A$. We say that $H$ is emph{$X$-quasipermutable } (emph{$X_{S}$-quasipermutable}, respectively) in $G$ provided $G$ has a subgroup$B$ such that $G=N_{G}(H)B$ and $H$ $X$-permutes with $B$ and with all subgroups (with all Sylowsubgroups, respectively) $...

red hot pepper is a plant that belongs to the solanaceae family and is known as capsicum annuum. capsaicin is the active ingredient of cayenne pepper. ghrelin is a hormone, which consists of polypeptide structure. ghrelin also contributes to growth hormone secretion, energy balance, food intake and body weight regulator. the aim of this study was the localization and expression of ghrelin in th...

in this paper we introduce and study an algebraic structure, namely grouplike. a grouplike is something between semigroup and group and its axioms are generalizations of the four group axioms. every grouplike is a semigroup containing the minimum ideal that is also a maximal subgroup (but the converse is not valid). the first idea of grouplikes comes from b-parts and $b$-addition of real number...

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,...

Let G be a finite group. Yakov Berkovic investigated the following concept: A subgroup H of G is called NR−subgroup with respect to G if A = AG ⋂ H for any subgroup A H.In particulary,called a finite group G NN−group if its any subgroup is either normal subgroup or NR−subgroup of G. In fact, all groups with order p -p3 are NN -group,where p is a prime. In this paper, the nature and structure of...

In this paper we introduce and study an algebraic structure, namely Grouplike. A grouplike is something between semigroup and group and its axioms are generalizations of the four group axioms. Every grouplike is a semigroup containing the minimum ideal that is also a maximal subgroup (but the converse is not valid). The first idea of grouplikes comes from b-parts and $b$-addition of real number...

In this article we introduce the notion of n-capable groups. It is shown that every group G admits a uniquely determined subgroup (〖Z^n)〗^* (G) which is a characteristic subgroup and lies in the n-centre subgroup of the group G. This is the smallest subgroup of G whose factor group is n-capable. Moreover, some properties of n-central extension will be studied.

Let G be a finite group and S proper subgroup of G. A is called an S-(CAP)-group if every local either CAP-subgroup or conjugate to
 S. The main purpose this construction to demonstrate new way analyzing the structure by properties number conjugacy classes its subgroups.

In this paper, we extend the construction of a fuzzy subgroup generated by a fuzzy subset to $L$-setting. This construction is illustrated by an example. We also prove that for an $L$-subset of a group, the subgroup generated by its level subset is the level subset of the subgroup generated by that $L$-subset provided the given $L$-subset possesses sup-property.