• Honam Mathematical Journal
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• v.28 no.1
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• pp.31-44
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• 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
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• v.46 no.3
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• pp.445-448
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• 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.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.169-176
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• 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.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.253-260
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• 2002

For an outer action $\alpha$ of a finite group G on a factor M, it was proved that H is a, normal subgroup of G if and only if there exists a finite group F and an outer action $\beta$ of F on the crossed product algebra M $\times$$_{\alpha}$ G = (M $\times$$_{\alpha}$ F. We generalize this to infinite group actions. For an outer action $\alpha$ of a discrete group, we obtain a Galois correspondence for crossed product algebras related to normal subgroups. When $\alpha$ satisfies a certain condition, we also obtain a Galois correspondence for fixed point algebras. Furthermore, for a minimal action $\alpha$ of a compact group G and a closed normal subgroup H, we prove $M^{G}$ = ( $M^{H}$)$^{{beta}(G/H)}$for a minimal action $\beta$ of G/H on $M^{H}$.f G/H on $M^{H}$.TEX> H/.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.781-799
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.723-730
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• 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.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.319-322
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• 1998

For an M-group G, it is shown that a normal subgroup of G whose order is coprime to its index is an M-group.

• Journal of Oral Medicine and Pain
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• v.11 no.1
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• pp.67-78
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• 1986

This study was attempted to identify the emotional characteristics of temporomandibular disorder patients. The author applied one of the self-report modes of psychological measurement, Symptom Chechlist-90-Revision. The subjects were 219 TM disorder patients who visited the Department of Oral Diagnosis and Oral Medicine, Seoul National University Hospital during the period from December 1985 to September 1986. All the patients were divided into subgroup according sex, age, duration of symptoms, presence or absence of T-scores of each symptom dimension and global index. The obtained result were as follows : 1. Mean value of T-scores of each symptom dimension and global of the overall patients was within normal range. The two higher mean values of T-scores among 9 symptom dimensions were those of SOM and ANX. 2. Mean values of T-scores of females were higher than those of males in the O-C, DEP, ANX, HOS, PSY dimensions and all global indices, and there was a significant difference in the distribution of T-scores of the SOM dimension between males and female(P<0.05). 3. There was no significant difference between the subgroup under 30 years and the subgroup 30 years or older. 4. The subgroup with symptoms for 6 months or longer showed the higher mean values of T-scorers in the SOM, O-C, I-S, DEP, ANX, PHOB, PAR, PSY dimensions and all global indices compared with the subgroup with symptoms for shorter than 6 months. 5. The subgroup with pain showed the higher mean values of T-scores in all the symptom dimensions except the PAR in comparison with the subgroup with other complaints than pain, and there was a significant difference in the distribution of T-scores of the PST index between the pain subgroup and the non-pain subgroup(P<0.05). There was a significant difference in the distribution of T-scores of the PHOB dimension between the high-school graduates subgroup and the college graduates subgroup(P<0.05).

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.181-189
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• 2011

Let G be a group and X be a nonempty set and H be a subgroup of G. For a given ${\phi}_G\;:\;G{\times}X{\rightarrow}X$, a group action of G on X, we define ${\phi}_H\;:\;H{\times}X{\rightarrow}X$, a subgroup action of H on X, by ${\phi}_H(h,x)={\phi}_G(h,x)$ for all $(h,x){\in}H{\times}X$. In this paper, by considering a subgroup action of H on X, we have some results as follows: (1) If H,K are two normal subgroups of G such that $H{\subseteq}K{\subseteq}G$, then for any $x{\in}X$ ($orb_{{\phi}_G}(x)\;:\;orb_{{\phi}_H}(x)$) = ($orb_{{\phi}_G}(x)\;:\;orb_{{\phi}_K}(x)$) = ($orb_{{\phi}_K}(x)\;:\;orb_{{\phi}_H}(x)$); additionally, in case of $K{\cap}stab_{{\phi}_G}(x)$ = {1}, if ($orb_{{\phi}_G}(x)\;:\;orb_{{\phi}H}(x)$) and ($orb_{{\phi}_K}(x)\;:\;orb_{{\phi}_H}(x)$) are both finite, then ($orb_{{\phi}_G}(x)\;:\;orb_{{\phi}_H}(x)$) is finite; (2) If H is a cyclic subgroup of G and $stab_{{\phi}_H}(x){\neq}$ {1} for some $x{\in}X$, then $orb_{{\phi}_H}(x)$ is finite.

• Pediatric Gastroenterology, Hepatology & Nutrition
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• v.19 no.1
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• pp.38-43
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• 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.