• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1147-1155
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• 2011

In J. Korean Math. Soc, Zhang, Xu and other authors investigated the following problem: what is the structure of finite groups which have many normal subgroups? In this paper, we shall study this question in a more general way. For a finite group G, we define the subgroup $\mathcal{A}(G)$ to be intersection of the normalizers of all non-cyclic subgroups of G. Set $\mathcal{A}_0=1$. Define $\mathcal{A}_{i+1}(G)/\mathcal{A}_i(G)=\mathcal{A}(G/\mathcal{A}_i(G))$ for $i{\geq}1$. By $\mathcal{A}_{\infty}(G)$ denote the terminal term of the ascending series. It is proved that if $G=\mathcal{A}_{\infty}(G)$, then the derived subgroup G' is nilpotent. Furthermore, if all elements of prime order or order 4 of G are in $\mathcal{A}(G)$, then G' is also nilpotent.

• Honam Mathematical Journal
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• v.20 no.1
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• pp.147-152
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• 1998

In this paper, we shall investigate the admittance of a fixed point free deformation(FPFD) on the locally nilpotent spaces when ${\pi}_1(X)$ is infinite. More precisely, for $X{\in}(S_{{\ast}{LN}})$ with ${\pi}_1(X)$ infinite, we prove the admittance of a FPFD where ${\pi}_1(X)$ has the maximal condition on normal subgroups, or ${\pi}_1(X)$ satisfies either the max-${\infty}$ or min-${\infty}$ for non-nilpotent subgroups where $S_{{\ast}{LN}}$ denotes the category of the locally nilpotent spaces and base point preserving continuous maps.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.5
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• pp.646-655
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• 2012

First, we prove a number of results about interval-valued fuzzy groups involving the notions of interval-valued fuzzy cosets and interval-valued fuzzy normal subgroups which are analogs of important results from group theory. Also, we introduce analogs of some group-theoretic concepts such as characteristic subgroup, normalizer and abelian groups. Secondly, we prove that if A is an interval-valued fuzzy subgroup of a group G such that the index of A is the smallest prime dividing the order of G, then A is an interval-valued fuzzy normal subgroup. Finally, we show that there is a one-to-one correspondence the interval-valued fuzzy cosets of an interval-valued fuzzy subgroup A of a group G and the cosets of a certain subgroup H of G.

• Honam Mathematical Journal
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• v.27 no.3
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• pp.369-388
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• 2005

First, we prove a number of results about intuitionistic fuzzy groups involving the notions of intuitionistic fuzzy cosets and intuitionistic fuzzy normal subgroups which are analogs of important results from group theory. Also, we introduce analogs of some group-theoretic concepts such as characteristic subgroup, normalizer and Abelian groups. Secondly, we prove that if A is an intuitionistic fuzzy subgroup of a group G such that the index of A is the smallest prime dividing the order of G, then A is an intuitionistic fuzzy normal subgroup. Finally, we show that there is a one-to-one correspondence the intuitionistic fuzzy cosets of an intuitionistic fuzzy subgroup A of a group G and the cosets of a certain subgroup H of G.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.181-191
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• 1999

We consider Bayesian models allow multiple grouping of parameters for the normal means estimation problem. In particular, we consider a typical Bayesian hierarchical approach based on thepartial exchangeability where the components within a subgroup are exchangeable, but the different subgroups are not. We discuss implementation of such Bayesian procedures via Gibbs sampling. We illustrate the proposed methods with numerical examples.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.795-826
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• 2005

We study free actions of finite abelian groups on 3­dimensional nilmanifolds. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal nilpotent subgroups of almost Bieberbach groups of finite index, up to affine conjugacy. All such actions are completely classified.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1411-1440
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• 2017

We study free actions of finite groups on 3-dimensional nil-manifolds with the first homology ${\mathbb{Z}}^2{\oplus}{\mathbb{Z}}_p$. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal nilpotent subgroups of almost Bieberbach groups of finite index, up to affine conjugacy.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1475-1479
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• 2020

Let G be a finite group and ${\sigma}_1(G)={\frac{1}{{\mid}G{\mid}}}\;{\sum}_{H{\leq}G}\;{\mid}H{\mid}$. Under some restrictions on the number of conjugacy classes of (non-normal) maximal subgroups of G, we prove that if ${\sigma}_1(G)<{\frac{117}{20}}$, then G is solvable. This partially solves an open problem posed in [9].

• The korean journal of orthodontics
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• v.34 no.3 s.104
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• pp.229-240
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• 2004

The purpose of this study was to evaluate the compensatory changes of occlusal plane angle in relation to skeletal factors. Lateral cephalograms of 61 adults with normal occlusion and 92 adults with skeletal malocclusions were traced and measured to analyze skeletal factors and occlusal plane angles. In terms of horizontal relationships, the normal occlusion group and malocclusion group were classified Into subgroups of skeletal Classes I, II, and III, while in terms of vertical relationships, each group was also classified into horizontal , average, and vertical subgroups. Some measurements were evaluated statistically by ANOVA and Post Hoc, and the others were reviewed by Paired t-tests. In this study, only the occlusal plane angle to AB plane did not show a significant difference between the normal occlusion group and malocclusion group. After treatment, the occlusal plane angle to the AB plane of the malocclusion group was approximated to that of normal occlusion group. The LOP to AB plane angle of the normal occlusion group was 91.7 in skeletal Class I, 88.8 in skeletal Class II, and 93.5 in skeletal Class III. This study was done to assess the treatment changes of the occlusal plane in the malocclusion group, and to draw a comparison with the normal occlusion group in order to present a reference to establish a new occlusal plane inclination.

• The Journal of Korean Medicine
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• v.22 no.3
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• pp.119-128
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• 2001

Objectives: Daechu (Dazhui: GV 14 (Governor Vessel))-point is located between the spinous process of the 7th cervical vertebra and that of the 1st thoracic vertebra. GV 14 has been used to treat high fever, neck pain, common cold, headache and so on. Fever may badly affect the improvement of stroke patients, so we investigated whether wet-cupping at GV 14 had effects on fever. Methods: In this study, 100 stroke patients were studied from Nov. 1999 to Oct. 2000. They were divided into the Sample group (n=49) and Control group (n=5l). The Sample group (n=49) was divided into Sample-Severe (n=2l), Sample-Mild (n=12), and Sample-Normal groups (n=16) and the Control group (n=5l) was divided into Control-Severe (n=8) and Control-Mild (n=43). We checked body temperature 6 times (just before treatment, after 30 ruin., 60, 90, 120 (2 hrs.), and 240 ruin. (4 hrs.)) in the Sample group and 3 times (just before treatment, after 120 min. (2 hrs.), and 240 ruin. (4 hrs.)) in the Control group. Results: In comparison with fever between before treatment and after 2 and 4 hours in each group, fever in the Sample subgroups decreased significantly in all cases, fever in the Control subgroups didn't decrease significantly in most cases except fever after 4 hours in the Control-Mild group. In comparison with fever differences between the Sample and Control group, fever of the Sample group more significantly decreased than that of the Control group in all comparisons. In comparison with fever among sample subgroups, fever of the Sample-Severe group decreased more than that of the Sample-Mild group but it was not significant. Conclusions: This study suggested that wet-cupping at GV 14 has significant effects on fever in stroke patients. We hope that this treatment will be used more widely as an emergent treatment.