• Korean Journal of Mathematics
• /
• 제26권3호
• /
• pp.373-385
• /
• 2018

In this paper we introduce the notion of a fuzzy kernel of a fuzzy homomorphism on groups and we show that it is a fuzzy normal subgroup of the domain group. Conversely, we also prove that any fuzzy normal subgroup is a fuzzy kernel of some fuzzy epimorphism, namely the canonical fuzzy epimorphism. Finally, we formulate and prove the fuzzy version of the fundamental theorem of homomorphism and those isomorphism theorems.

• 대한수학회보
• /
• 제50권2호
• /
• pp.445-449
• /
• 2013

We consider a congruence ${\rho}$ on a group G as a subsemigroup of the direct product $G{\times}G$. It is well known that a relation ${\rho}$ on G is a congruence if and only if there exists a normal subgroup N of G such that ${\rho}=\{(s,\;t):st^{-1}{\in}N\}$. In this paper we prove that if G is a finitely presented group, and if N is a normal subgroup of G with finite index, then the congruence ${\rho}=\{(s,\;t):st^{-1}{\in}N\}$ on G is finitely presented.

• 대한수학회보
• /
• 제60권5호
• /
• pp.1375-1390
• /
• 2023

In this note, we shall show that the generalized free products of subgroup separable groups amalgamating a subgroup which itself is a finite extension of a finitely generated normal subgroup of both the factor groups are weakly potent and cyclic subgroup separable. Then we apply our result to generalized free products of finite extensions of finitely generated torsion-free nilpotent groups. Finally, we shall show that their tree products are cyclic subgroup separable.

• 호남수학학술지
• /
• 제28권1호
• /
• pp.31-44
• /
• 2006

We discuss various types of sublattice of the lattice of intuitionistic fuzzy subgroups of a given group. We prove that a special class of intuitionitic fuzzy normal subgroups constitutes a modular sublattice of the lattice of intuitionistic fuzzy subgroups.

• Kyungpook Mathematical Journal
• /
• 제46권3호
• /
• pp.445-448
• /
• 2006

Let N be a normal subgroup of a path-connected topological group (G, $t$). In this paper, the authors consider the existence of path-connectedness in refined topologies in order to address the property of maximal path-connectedness in topological groups. In particular, refinements on $t$ and refinements on the quotient topology on G/N are studied. The preservation of path-connectedness in extending topologies and translation topologies is also considered.

• Journal of applied mathematics & informatics
• /
• 제18권1_2호
• /
• pp.657-663
• /
• 2005

In this paper, we consider groups of permutations S on a set A acting on subsets X of A. In particular, we show that if $X_2{\subseteq}X_1{\subseteq}A$ and Y is an S-normal extension of $X_2 in X_1$, then the Galois group $G_{S}(X_1/Y){\;}of{\;}X_1{\;}over{\;}X_2$ relative to S is an S-closed subgroup of $G_{S}(X_1/X_2)$ in the setting of a Galois theory (correspondence) for this situation.

• Journal of applied mathematics & informatics
• /
• 제41권4호
• /
• pp.781-799
• /
• 2023

For any bipolar multi Q-fuzzy set δ of an universe set G, we redefined a normal, conjugate concepts, union and product operations of a bipolar M - N-multi Q-fuzzy subgroups and we discuss some of its properties. On the other hand, we introduce and define the level subsets positive β-cut and negative α-cut of bipolar M - N- multi Q- fuzzy subgroup and discuss some of its related properties.

• Korean Journal of Mathematics
• /
• 제5권2호
• /
• pp.169-176
• /
• 1997

The purpose of this note is to compare two known results related to the lifting problem of an action of a topological group G on a G-space X to a coverring space of X.

• 대한수학회보
• /
• 제41권4호
• /
• pp.723-730
• /
• 2004

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

• Pediatric Gastroenterology, Hepatology & Nutrition
• /
• 제19권1호
• /
• pp.38-43
• /
• 2016

Purpose: Each ethnic group has a unique life style, including diets. Life style affects bowel movement. The aim of this study is to describe the results of colon transit time (CTT) tests in Korean children who had chronic functional constipation based on highly refined data. Methods: One hundred ninety (86 males) out of 415 children who performed a CTT test under the diagnosis of chronic constipation according to Rome III criteria at Konkuk University Medical Center from January 2006 through March 2015 were enrolled in this study. Two hundreds twenty-five children were excluded on the basis of CTT test result, defecation diary, and clinical setting. Shapiro-Wilk and Mann-Whitney U, and chi-square tests were used for statistical analysis. Results: The median value and interquartile range (IQR) of CTT was 54 (37.5) hours in Encopresis group, and those in non-encopresis group was 40.2 (27.9) hours (p<0.001). The frequency of subtype between non-encopresis group and encopresis was statistically significant (p=0.002). The non-encopresis group (n=154, 81.1%) was divided into normal transit subgroup (n=84, 54.5%; median value and IQR of CTT=26.4 [9.6] hours), outlet obstruction subgroup (n=18, 11.7%; 62.4 [15.6] hours), and slow transit subgroup (n=52, 33.8%; 54.6 [21.0] hours]. The encopresis group (n=36, 18.9%) was divided into normal transit subgroup (n=8, 22.2%; median value and IQR of CTT=32.4 [9.9] hours), outlet obstruction subgroup (n=8, 22.2%; 67.8 [34.8] hours), and slow transit subgroup (n=20, 55.6%; 59.4 [62.7] hours). Conclusion: This study provided the basic pattern and value of the CTT test in Korean children with chronic constipation.