• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.461-466
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• 2016

In general, polygonal products of free groups are not residually finite. Using the residual finiteness of polygonal products of nilpotent groups, we show that certain polygonal products of free groups are residually finite.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.813-828
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• 2013

It is known that generalized free products of finitely generated nilpotent groups are conjugacy separable when the amalgamated subgroups are cyclic or central in both factor groups. However, those generalized free products may not be conjugacy separable when the amalgamated subgroup is a direct product of two infinite cycles. In this paper we show that generalized free products of finitely generated nilpotent groups are conjugacy separable when the amalgamated subgroup is ${\langle}h{\rangle}{\times}D$, where D is in the center of both factors.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.521-530
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• 1997

We first prove a criterion for the conjugacy separability of free products with amalgamation where the amalgamated subgroup is not necessarily cyclic. Applying this result, we show that free products of finite number of polycyclic-by-finite groups with central amalgamation are conjugacy separable. We also show that polygonal products of polycyclic-by-finite groups, amalgamating central cyclic subgroups with trivial intersections, are conjugacy separable.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1375-1390
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• 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.

• Kyungpook Mathematical Journal
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• v.48 no.3
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• pp.495-502
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• 2008

We show that free products of finitely generated and residually p-finite nilpotent groups, amalgamating p-closed central subgroups are residually p-finite. As a consequence, we are able to show that generalized free products of residually p-finite abelian groups are residually p-finite if the amalgamated subgroup is closed in the pro-p topology on each of the factors.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1195-1204
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• 2010

In this paper, we prove a criterion of conjugacy separability of generalized free products of polycyclic-by-finite groups with a non cyclic amalgamated subgroup. Applying this criterion, we prove that certain generalized free products of polycyclic-by-finite groups are conjugacy separable.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.949-959
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• 2012

In general, a class-preserving automorphism of generalized free products of nilpotent groups, amalgamating a cyclic normal subgroup of order 8, need not be an inner automorphism. We prove that every class-preserving automorphism of generalized free products of nitely generated nilpotent groups, amalgamating a cyclic normal subgroup of order less than 8, is inner.

• Bulletin of the Korean Mathematical Society
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• v.47 no.5
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• pp.997-1000
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• 2010

We prove that the reduced free product of $k\;{\times}\;k$ matrix algebras over abelian $C^*$-algebras is not the minimal tensor product of reduced free products of $k\;{\times}\;k$ matrix algebras over abelian $C^*$-algebras. It is shown that the reduced group $C^*$-algebra associated with a group having the property T of Kazhdan is not isomorphic to a reduced free product of abelian $C^*$-algebras or the minimal tensor product of such reduced free products. The infinite tensor product of reduced free products of abelian $C^*$-algebras is not isomorphic to the tensor product of a nuclear $C^*$-algebra and a reduced free product of abelian $C^*$-algebra. We discuss the freeness of free product $II_1$-factors and solidity of free product $II_1$-factors weaker than that of Ozawa. We show that the freeness in a free product is related to the existence of Cartan subalgebras in free product $II_1$-factors. Finally, we give a free product factor which is not solid in the weak sense.

• Proceedings of the International Microelectronics And Packaging Society Conference
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• 2004.09a
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• pp.93-99
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• 2004

At present, LG Electronics pushes ahead to eliminate the Pb(Lead) -a hazardous material- from all products. Especially, we have performed to select the optimum standard composition of lead free alloy for the application to products for about 3 years from 2000. These days, we have the chance for applying to the mass-production. This project constructed the system for applying the lead free solders on consumer electronic products, which is one of the major products of the LG Electronics. To select the lead free solders with corresponding to the product features, we have passed through the test and applied with Sn-3.0Ag-0.5Cu alloy system to our products, and for the application to the high melting temperature composition, we secured the thermal resistance of the many parts and substrate and optimized the processing conditions. We have operated the temperature cycling test and the high temperature storage test under the standards to confirm the reliability of the products. On these samples, we considered the consequence of our decision by the operating test. For the long life time of the product, we have operated the temperature cycling test at $-45^{\circ}C-+125^{\circ}C$, 1 cycle/hour, 1000 cycles. Also we have tested the tin whisker growth about lead free plating on lead finish. We have analyzed with the SEM, EDS and any other equipment for confirming the failure mode at the joint and the tin whisker growth on lead free finish.

• Journal of Dairy Science and Biotechnology
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• v.38 no.1
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• pp.1-18
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• 2020

Lactose intolerance is a pathophysiological phenomenon caused by a deficiency of the enzyme lactase present in human intestines. Changes in intestinal digestion and colon fermentation after the intake of lactose-containing products cause diarrhea and other clinical discomforts. Therefore, lactose intolerance can be easily ameliorated by consuming lactose hydrolyzed milk and dairy products. In the recent years, lactose-free dairy products have provided lactose intolerant consumers with several options, due to an improvement in the quality and an increase in the variety of products. Currently, the manufacturing of lactose-free products also represents the fastest growing sector in the dairy industry. This review, thus, aims to provide an overview of the current availability and prospects of lactose-free dairy products, and also discuss the potential benefits of the development of a variety of lactose-free dairy foods.