We study the definability of certain subgroups of a group G that does not have the independence property. If a (type) definable subset X of an elementary extension G of G has property P , we call its trace X∩G over G an externally (type) definable P set. We show the following. Centralisers of subsets of G are externally definable subgroups. Cores of externally definable subgroups and iterated c...

Objective(s) To determine the potential toxic effects of manual soldering flux cored solder wire on lung of the rat as an experimental model. Materials and Methods A total number of 48 adult male rats were divided into experimental (n= 30) and control (n= 18) groups. Based on exposure time to solder fume, each group was further subdivided into 2, 4 and 6 week subgroups. Rats of experimental ...

Let S∞ denote the symmetric group on the natural numbers N. Then S∞ is a Polish group with the topology inherited from NN with the product topology and the discrete topology on N. Let d denote the least cardinality of a dominating family for NN and let c denote the continuum. Using theorems of Galvin, and Bergman and Shelah we prove that if G is any subgroup of S∞ that is closed in the above to...

Objective(s): The present study aimed to assess the in-vitro efficacy of nanoparticulate calcium sodium phosphosilicate mouthwash in the obstruction of dentinal tubules.Materials and Methods: This in-vitro, study was conducted on 120 sections obtained from extracted human premolars, which were etched with citric acid for two minutes and rinsed with distilled water. Afterwards, the section...

in this paper, we introduce some properties of an intuitionistic normal fuzzy m-subgroup of m- group with m-homomorphism and isomorphism. we study he image, the pre-image and the inverse mapping of the intuitionistic normal fuzzy m-‎subgroups.‎

In this paper, we count the number of fuzzy subgroups of cyclic group G = Zp × Zq × Zr × Zs with p, q, r, s are distinct prime numbers. We define an equivalence relation on the fuzzy subgroups of any groups G and determine all of its subgroups. Then we draw the diagram of lattice subgroups of G. The number of fuzzy subgroups of G by observing the diagram then will be counted. Mathematics Subjec...

a subgroup $h$ is said to be $s$-permutable in a group $g$‎, ‎if‎ ‎$hp=ph$ holds for every sylow subgroup $p$ of $g$‎. ‎if there exists a‎ ‎subgroup $b$ of $g$ such that $hb=g$ and $h$ permutes with every‎ ‎sylow subgroup of $b$‎, ‎then $h$ is said to be $ss$-quasinormal in‎ ‎$g$‎. ‎in this paper‎, ‎we say that $h$ is a weakly $ss$-quasinormal‎ ‎subgroup of $g$‎, ‎if there is a normal subgroup ...

Let Mod(S) be the extended mapping class group of a surface S. For S the twice-punctured torus, we show that there exists an isomorphism of finite index subgroups of Mod(S) which is not the restriction of any inner automorphism. For S a torus with at least three punctures, we show that every injection of a finite index subgroup of Mod(S) into Mod(S) is the restriction of an inner automorphism o...

a subgroup $h$ is said to be $s$-permutable in a group $g$‎, ‎if‎ ‎$hp=ph$ holds for every sylow subgroup $p$ of $g$‎. ‎if there exists a‎ ‎subgroup $b$ of $g$ such that $hb=g$ and $h$ permutes with every‎ ‎sylow subgroup of $b$‎, ‎then $h$ is said to be $ss$-quasinormal in‎ ‎$g$‎. ‎in this paper‎, ‎we say that $h$ is a weakly $ss$-quasinormal‎ ‎subgroup of $g$‎, ‎if there is a normal subgroup ...