for a composition $lambda$ of $n$ our aim is to obtain reduced forms ‎for all the elements in the kazhdan-lusztig (right) cell containing ‎$w_{j(lambda)}$‎, ‎the longest element of the standard parabolic‎ ‎subgroup of $s_n$ corresponding to $lambda$‎. ‎we investigate how far this is possible to achieve by looking at‎ ‎elements of the form $w_{j(lambda)}d$‎, ‎where $d$ is a prefix of ‎an element...

suppose that $h$ is a subgroup of $g$‎, ‎then $h$ is said to be‎ ‎$s$-permutable in $g$‎, ‎if $h$ permutes with every sylow subgroup of‎ ‎$g$‎. ‎if $hp=ph$ hold for every sylow subgroup $p$ of $g$ with $(|p|‎, ‎|h|)=1$)‎, ‎then $h$ is called an $s$-semipermutable subgroup of $g$‎. ‎in this paper‎, ‎we say that $h$ is partially $s$-embedded in $g$ if‎ ‎$g$ has a normal subgroup $t$ such that $ht...

The concept of vague graph was introduced by Ramakrishna in [12]. A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. The main purpose of this paper is to introduce the concept of dominating set, perfect dominating set, minimal perfect dominating set and i...

bentea and tu{a}rnu{a}uceanu~(an. c{s}tiinc{t}. univ. al. i.cuza iac{s}, ser. nouv{a}, mat., {bf 54(1)} (2008), 209-220)proposed the following problem: find an explicit formula for thenumber of fuzzy subgroups of a finite hamiltonian group of type$q_8times mathbb{z}_n$ where $q_8$ is the quaternion group oforder $8$ and $n$ is an arbitrary odd integer. in this paper weconsider more general grou...

in this paper, we compute the number of fuzzy subgroups of some classes of non-abeilan groups. explicit formulas are givenfor dihedral groups $d_{2n}$, quasi-dihedral groups $qd_{2^n}$, generalized quaternion groups $q_{4n}$ and modular $p$-groups $m_{p^n}$.

In order to model the real world with imprecise and uncertain information, various extensions of the classical relational data model have been studied in literature using fuzzy set theory. However, vague set, as a generalized fuzzy set, has more powerful ability to process fuzzy information than fuzzy set. In this paper, we have proposed a vague relational database model and have defined a new ...

Let H be a subgroup of a group G. H is said to be S-embedded in G if G has a normal T such that HT is an S-permutable subgroup of G and H ∩ T ≤ H sG, where H denotes the subgroup generated by all those subgroups of H which are S-permutable in G. In this paper, we investigate the influence of minimal S-embedded subgroups on the structure of finite groups. We determine the structure the finite grou...