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.

Despite their versatility, only a few single-crystal X-ray structures of lead carboxylates exist, due to difficulties with solubility. In particular, the structures of long-chain metal carboxylates have not been reported. The lone electron pair in Pb(ii) can be stereochemically active or inactive, leading to two types of coordination geometries commonly referred to as hemidirected and holodirec...

Fig (Ficus carica) trees exhibited symptoms of little leaf, mottling and deformation in Sanliurfa province, Turkey. Poylmerase chain reaction (PCR) through direct nested-PCR, phylogeny based on the sequence analysis revealed that infecting agent was closely related to ‘Candidatus Phytoplasma aurantifolia’ (16SrII-B subgroup). This is first report Ca. P. aurantifolia fig

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.

 ‎Let $tilde{F}=(Q,S,tilde{R},Z,omega,tilde{delta},‎ F_1,F_2)$‎ ‎be a general fuzzy automaton and the set of its states be a group.‎ ‎The aim of this paper is the study of applications of a group in a‎ ‎general fuzzy automaton‎. ‎For this purpose‎, ‎we define the concepts‎ ‎of fuzzy normal kernel of a general fuzzy automaton‎, ‎fuzzy kernel‎ ‎of a general fuzzy automaton‎, ‎adjustable‎, ‎multip...

In this paper we classify fuzzy subgroups of a rank-3 abelian group $G = mathbb{Z}_{p^n} + mathbb{Z}_p + mathbb{Z}_p$ for any fixed prime $p$ and any positive integer $n$, using a natural equivalence relation given in cite{mur:01}. We present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) non-isomorp...

In this study, we evaluated the associations between the V4 (rs2787094 G>C) polymorphism in a disintegrin and metalloproteinase domain 33 (ADAM33) gene and asthma risk. We searched Web of Science, PubMed, Google Scholar, EBSCO, Cochrane Library, and CBM databases from inception through August 2013, without language restrictions. Meta-analysis was performed using the STATA 12.0 software. Crude o...

Gaillardia plants exhibiting symptoms characteristic of viral and phytoplasmal diseases were collected at botanical gardens and floriculture farms in Lithuania. Cucumber mosaic cucumovirus was isolated from diseased plants exhibiting symptoms characterized by stunting, flower breaking and malformation of petals. The virus was characterized based on electron microscopy, serology, reactions of in...

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 $G$.