• Title/Summary/Keyword: S-closed subgroup

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GALOIS GROUPS FOR PERMUTATIONS ON SETS

  • PARK HONG GOO
    • Journal of applied mathematics & informatics
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    • v.18 no.1_2
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    • pp.657-663
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    • 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.

An application of least area surfaces to 3-manifolds

  • Moon, Myoung-Ho
    • Communications of the Korean Mathematical Society
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    • v.11 no.3
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    • pp.797-805
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    • 1996
  • We provide a new proof of the following fact using least area surfaces : If the fundamental group of a $P^2$-irreducible closed 3-manifold M contains a finitely generated nontrivial normal subgroup of infinite index, then M has a finite cover which is a closed surface bundle over $S^1$ , unless N is free.

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APPROXIMATE FIBRATIONS AND NON-APPROXIMATE FIBRATIONS IN PL CATEGORY

  • Im, Young-Ho
    • Communications of the Korean Mathematical Society
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    • v.11 no.4
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    • pp.1077-1085
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    • 1996
  • This paper provides examples which can not be approximate fibrations and shows that if $N^n$ is a closed aspherical manifold, $\pi_1(N)$ is hyperhophian, normally cohophian, and $\pi_1(N)$ has no nontrivial Abelian normal subgroup, then the product of $N^n$ and a sphre $S^m$ satisfies the property that all PL maps from an orientable manifold M to a polyhedron B for which each point preimage is homotopy equivalent to $N^n \times S^m$ necessarily are approximate fibrations.

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A Study of Intangible Cultural Heritage Communities through a Social Network Analysis - Focused on the Item of Jeongseon Arirang - (소셜 네트워크 분석을 통한 무형문화유산 공동체 지식연결망 연구 - 정선아리랑을 중심으로 -)

  • Oh, Jung-shim
    • Korean Journal of Heritage: History & Science
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    • v.52 no.3
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    • pp.172-187
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    • 2019
  • Knowledge of intangible cultural heritage is usually disseminated through word-of-mouth and actions rather than written records. Thus, people assemble to teach others about it and form communities. Accordingly, to understand and spread information about intangible cultural heritage properly, it is necessary to understand not only their attributes but also a community's relational characteristics. Community members include specialized transmitters who work under the auspices of institutions, and general transmitters who enjoy intangible cultural heritage in their daily lives. They converse about intangible cultural heritage in close relationships. However, to date, research has focused only on professionals. Thus, this study focused on the roles of general transmitters of intangible cultural heritage information by investigating intangible cultural heritage communities centering around Jeongseon Arirang; a social network analysis was performed. Regarding the research objectives presented in the introduction, the main findings of the study are summarized as follows. First, there were 197 links between 74 members of the Jeongseon Arirang Transmission Community. One individual had connections with 2.7 persons on average, and all were connected through two steps in the community. However, the density and the clustering coefficient were low, 0.036 and 0.32, respectively; therefore, the cohesiveness of this community was low, and the relationships between the members were not strong. Second, 'Young-ran Yu', 'Nam-gi Kim' and 'Gil-ja Kim' were found to be the prominent figures of the Jeongseon Arirang Transmission Community, and the central structure of the network was concentrated around these three individuals. Being located in the central structure of the network indicates that a person is popular and ranked high. Also, it means that a person has an advantage in terms of the speed and quantity of the acquisition of information and resources, and is in a relatively superior position in terms of bargaining power. Third, to understand the replaceability of the roles of Young-ran Yu, Nam-gi Kim, and Gil-ja Kim, who were found to be the major figures through an analysis of the central structure, structural equivalence was profiled. The results of the analysis showed that the positions and roles of Young-ran Yu, Nam-gi Kim, and Gil-ja Kim were unrivaled and irreplaceable in the Jeongseon Arirang Transmission Community. However, considering that these three members were in their 60s and 70s, it seemed that it would be necessary to prepare measures for the smooth maintenance and operation of the community. Fourth, to examine the subgroup hidden in the network of the Jeongseon Arirang Transmission Community, an analysis of communities was conducted. A community refers to a subgroup clearly differentiated based on modularity. The results of the analysis identified the existence of four communities. Furthermore, the results of an analysis of the central structure showed that the communities were formed and centered around Young-ran Yu, Hyung-jo Kim, Nam-gi Kim, and Gil-ja Kim. Most of the transmission TAs recommended by those members, students who completed a course, transmission scholarship holders, and the general members taught in the transmission classes of the Jeongseon Arirang Preservation Society were included as members of the communities. Through these findings, it was discovered that it is possible to maintain the transmission genealogy, making an exchange with the general members by employing the present method for the transmission of Jeongseon Arirang, the joint transmission method. It is worth paying attention to the joint transmission method as it overcomes the demerits of the existing closed one-on-one apprentice method and provides members with an opportunity to learn their masters' various singing styles. This study is significant for the following reasons: First, by collecting and examining data using a social network analysis method, this study analyzed phenomena that had been difficult to investigate using existing statistical analyses. Second, by adopting a different approach to the previous method in which the genealogy was understood, looking at oral data, this study analyzed the structures of the transmitters' relationships with objective and quantitative data. Third, this study visualized and presented the abstract structures of the relationships among the transmitters of intangible cultural heritage information on a 2D spring map. The results of this study can be utilized as a baseline for the development of community-centered policies for the protection of intangible cultural heritage specified in the UNESCO Convention for the Safeguarding of Intangible Cultural Heritage. To achieve this, it would be necessary to supplement this study through case studies and follow-up studies on more aspects in the future.