• Title/Summary/Keyword: generalized free products

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CONJUGACY SEPARABILITY OF CERTAIN GENERALIZED FREE PRODUCTS OF NILPOTENT GROUPS

  • Kim, Goansu;Tang, C.Y.
    • 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.

CONJUGACY SEPARABILITY OF GENERALIZED FREE PRODUCTS OF FINITELY GENERATED NILPOTENT GROUPS

  • Zhou, Wei;Kim, Goan-Su;Shi, Wujie;Tang, C.Y.
    • 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.

CLASS-PRESERVING AUTOMORPHISMS OF GENERALIZED FREE PRODUCTS AMALGAMATING A CYCLIC NORMAL SUBGROUP

  • Zhou, Wei;Kim, Goan-Su
    • 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.

Residual P-Finiteness of Certain Generalized Free Products of Nilpotent Groups

  • Kim, Goan-Su;Lee, Young-Mi;McCarron, James
    • 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.

WEAK POTENCY AND CYCLIC SUBGROUP SEPARABILITY OF CERTAIN FREE PRODUCTS AND TREE PRODUCTS

  • Muhammad Sufi Mohd Asri;Wan Ainun Mior Othman;Kok Bin Wong;Peng Choon Wong
    • 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.

CONJUGACY SEPARABILITY OF FREE PRODUCTS WITH AMALGAMATION

  • Kim, Goan-Su
    • 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.

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OUTER AUTOMORPHISM GROUPS OF POLYGONAL PRODUCTS OF CERTAIN CONJUGACY SEPARABLE GROUPS

  • Kim, Goan-Su;Tang, Chi Yu
    • Journal of the Korean Mathematical Society
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    • v.45 no.6
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    • pp.1741-1752
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    • 2008
  • Grossman [7] showed that certain cyclically pinched 1-relator groups have residually finite outer automorphism groups. In this paper we prove that tree products of finitely generated free groups amalgamating maximal cyclic subgroups have residually finite outer automorphism groups. We also prove that polygonal products of finitely generated central subgroup separable groups amalgamating trivial intersecting central subgroups have residually finite outer automorphism groups.

OUTER AUTOMORPHISM GROUPS OF CERTAIN POLYGONAL PRODUCTS OF GROUPS

  • Kim, Goan-Su
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.1
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    • pp.45-52
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    • 2008
  • We show that certain polygonal products of any four groups, amalgamating central subgroups with trivial intersections, have Property E. Using this result, we derive that outer automorphism groups of polygonal products of four polycyclic-by-finite groups, amalgamating central subgroups with trivial intersections, are residually finite.

CFD aided design of the continuous casting tundish (전산유체기법을 이용한 연속주조 Tundish 의 형상 설계)

  • Cho J. R.;Ha M. Y.;Lee S. W.
    • Journal of computational fluids engineering
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    • v.2 no.1
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    • pp.117-128
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    • 1997
  • Effects of dam and weir on the fluid flow and behavior of inclusions in the continuous casting tundish have been studied using the CFD (Computational Fluid Dynamics) technique. Inclusions affecting the quality of steel products have been considered to be passive: the fluid flow has been obtained for unstaggered grid points defined on body-fitted generalized cuvilinear coordinates with no attention on inclusions, and the spatial propagation of inclusions has been determined by using the flow field data. The result show that the dam and weir direct the flow to the free surface and increase the residence time of inclusions significantly, and thereby that inclusions have much more chance to be floated to the free surface of the tundish where it is eliminated. It is also found that they offer more margin on the geometric design of exit nozzles connected to moulds. This finding is particularly important for twin casting operations where the quality of steel products from the two moulds be kept uniformly.

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Three-dimensional numerical simulation for the prediction of product shape in sheet casting process

  • Chae, Kyung-Sun;Lee, Mi-Hye;Lee, Seong-Jae;Lee, Seung-Jong
    • Korea-Australia Rheology Journal
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    • v.12 no.2
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    • pp.107-117
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    • 2000
  • Prediction of the product shape in sheet casting process is performed from the numerical simulation. A three-dimensional finite element method is used to investigate the flow behavior and to examine the effects of processing conditions on the sheet produced. Effects of inertia, gravity, surface tension and non-Newtonian viscosity on the thickness profile of the sheet are considered since the edge bead and the flow patterns in the chill roll region have great influence on the quality of the products. In the numerical simulation with free surface flows, the spine method is adopted to update the free surface, and the force-free boundary condition is imposed along the take-up plane to avoid severe singularity problems existing at the take-up plane. From the numerical results of steady isothermal flows of a generalized Newtonian fluid, it is shown that the draw ratio plays a major role in predicting the shape of the final sheet produced and the surface tension has considerable effect on the bead thickness ratio and the bead width fraction, while shear-thinning and/or tension-thickening viscosity affect the degree of neck-in.

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