• 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.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.811-827
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• 2000

We find some conditions to derive the conjugacy separability of the free product of conjugacy separable split extensions amalgamated along cyclic retracts. These conditions hold for any double coset separable groups and free-by-cyclic groups with nontrivial center. It was known that free-by-finite, polycyclic-by-finite, and fuchsian groups are double coset separable. Hence free products of those groups amalgamated along cyclic retracts are conjugacy separable.

• Journal of Nutrition and Health
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• v.20 no.4
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• pp.225-236
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• 1987

This study was performed to investigate the effects of lead poisoning and different levels of dietary lipid on lead and lipid metabolism in the rats. Forty eight male weanling rats of Sprague-Dawley strain weighing 73.1$\pm$11.1g were blocked into 6 groups according to body weight. Dietary lipid were given at the lev딘 of 5, 20 and 40% of total caloric intake and lead were either administered or not. The results obtained are summerized as follows ; 1) Food intake, weight gain, F.E.R. liver and epididymal. fat pad weights, weight and length of bone, hematocrit and hemoglobin content in Pb-adminstered groups were lower than these in Pb-free groups. 2) Plasma lipid and cholesterol levels were tended to be higher in Pb-administered groups than in Pb-free groups, while liver lipid and cholesterol levels were tended to be lower in Pb-adminstered groups. 3) Fecal dry matter excretion was tended to be higher in Pb-adminstered groups than in Pb-free groups, and were increased with increasing dietary lipid level. Daily fecal excretions of lipid and cholesterol were higher in high lipid groups than in low lipid groups and these levels were even higher in the animals exposed to Pb than in Pb-free groups. 4) Pb contents in blood, liver, kidney and bone were significantly higher in Pb administered groups than in Pb-free groups. Pb levels of blood, liver and bone did not show any significant difference among groups with different levels of dietary lipid, but Pb concentration in kidney of Pb-adminstered groups increased with increasing dietary lipid level.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.453-467
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• 1997

A transitive permutation representation of a group G is said to be multiplicity-free if all of its irreducible constituents are distinct. The character corresponding to the action is called the permutation character, given by $(1_H)^G$, where H is the stabilizer of a point. Multiplicity-free permutation characters are of interest in the study of centralizer algebras and distance-transitive graphs, and all finite simple groups are known to have such characters. In this article, we extend to the alternating groups the result of J. Saxl who determined the multiplicity-free permutation representations of the symmetric groups. We classify all subgroups H for which $(1_H)^An, n > 18$, is multiplicity-free.

• 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.51 no.4
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• pp.1205-1210
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• 2014

Let E be a free product of a finite number of cyclic groups, and S a normal subgroup of E such that $$E/S{\sim_=}G$$ is finite. For a prime p, $\hat{S}=S/S^{\prime}S^p$ may be regarded as an $F_pG$-module via conjugation in E. The aim of this article is to prove that $\hat{S}$ is decomposable into two indecomposable modules for finite elementary abelian p-groups G.

• Journal of Nutrition and Health
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• v.17 no.1
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• pp.68-77
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• 1984

The present study was designed to observe the effects of soyprotein and casein with or without cholesterol on serum and liver lipids in male rats. The 6 experimental groups were as fellows ; SF ; soyprotein, cholesterol-free diet. SC ; soyprotein, 0.5% cholesterol added diet. CF ; casein, cholesterol-free diet CC ; casein,0.5% cholesterol added diet. SCF ; protein mixture of soyprotein and casein(1 : 1), cholesterol-free diet SCC ; mixed protein, 0.5% cholesterol added diet. The hypocholesterolemic and hypotriglyceridemic effects of soyprotein were observed at 3 weeks, but these effects disappeared at 6 weeks. The hypocholesterolemic effect of soyprotein was more obvious when the 0.5% cholesterol was supplemented in the diets. The serum free cholesterol level was not affected by the dietary protein source or the dietary cholesterol, therefore, the difference in serum total cholesterol among groups seems due to the difference in cholesterol esters. There was a tendency of a higher percentage of HDL in soyprotein groups compared to casein groups at 1 week, however, this tendency disappeared with time. The liver cholesterol and triglyceride contents were not differ among cholesterol-free diet groups, however, with addition of cholesterol, those of soyprotein groups were significantly lower than casein groups. The higher serum arginine/lysine ratio of soyprotein groups may offer the part of explanation of its hypocholesterolemic effect.

• 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.