• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.143-148
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• 2001

First, we show the finiteness property of the homotopy fixed point set of p-discrete toral group. Let $G_\infty$ be a p-discrete toral group and X be a finite complex with an action of $G_\infty such that X^K$ is nilpotent for each finit p-subgroup K of $G_\infty$. Assume X is $F_\rho-complete$. Then X(sup)hG$\infty$ is F(sub)p-finite. Using this result, we give the condition so that X$^{hG}$ is $F_\rho-finite for \rho-compact$ toral group G.

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.309-317
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• 2003

In this paper we study the relation of Euler characteristic with respect to cohomology with compact support in F$_{p}$-coefficient for the fibration of ENR's and generalize some properties on proper G-spaces for locally compact Lie group G.G.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.719-725
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• 2001

For a p-compact group G, if G-space X is of finite S-type then we show that the localization $S^{-1}H^*(X_{hG})$is zero. By using this result, we prove the localization theorem for the pair G-space (X, A)

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.299-309
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• 2010

The Weyl group of a compact connected Lie group is a reflection group. If such Lie groups are locally isomorphic, the representations of the Weyl groups are rationally equivalent. They need not however be equivalent as integral representations. Turning to the invariant theory, the rational cohomology of a classifying space is a ring of invariants, which is a polynomial ring. In the modular case, we will ask if rings of invariants are polynomial algebras, and if each of them can be realized as the mod p cohomology of a space, particularly for dihedral groups.

• Restorative Dentistry and Endodontics
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• v.26 no.6
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• pp.485-491
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• 2001

The purpose of this study was to compare the mechanical properties of three condensable composite resins and one hybrid composite resin. The compressive strength, diametral tensile strength, Vicker's microhardness were tested for mechanical properties of condensable composite resins (SureFil, Ariston pHc, Synergy compact), and hybrid composite resin (Z 100). The tested materials were divided into four groups: control group Z 100 (3M Co. USA), experimental group I Ariston pHc, (Vivadent, Co., Liechtenstein) experimental group II SureFil (Dentsply, Co., U.S.A.), experimental group III Synergy Compact (Coltene, Co., Swiss). According to the above classification, we made samples of SureFil, Ariston pHc, Synergy Compact, Z 100 with separable cylindrical metal mold. And then, we measured and compared the value of compressive strength, diametral tensile strength and Vicker's microhardness of each sample. (omitted)

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.755-762
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• 1999

Let X be a p-compace groyp, Y -> X bd a p-compact-subgroup of X and G -> X be a p-compact toral subgroup of X with $(X/Y)^{hG} \neq 0$. In this paper we show that the homotopy fixed point set of the homotopy fibre $(X/Y)^{hG}$ is $F_p$-finite.

• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.171-180
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• 2018

In this paper, the necessary and sufficient conditions are considered for biprojectivity of Banach algebras $E_p(I)$. As an application, we investigate biprojectivity of convolution Banach algebras A(G) and $L^2(G)$ on a compact group G.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.307-317
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• 2010

In this paper we find necessary and sufficient conditions for weak amenability of the convolution Banach algebras A(K) and $L^2(K)$ for a compact hypergroup K, together with their applications to convolution Banach algebras $L^p(K)$ ($2\;{\leq}\;p\;<\;{\infty}$). It will further be shown that the convolution Banach algebra A(G) for a compact group G is weakly amenable if and only if G has a closed abelian subgroup of finite index.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.207-218
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• 2020

Some modular representations of reflection groups related to Weyl groups are considered. The rational cohomology of the classifying space of a compact connected Lie group G with a maximal torus T is expressed as the ring of invariants, H*(BG; ℚ) ≅ H*(BT; ℚ)^W(G), which is a polynomial ring. If such Lie groups are locally isomorphic, the rational representations of their Weyl groups are equivalent. However, the integral representations need not be equivalent. Under the mod p reductions, we consider the structure of the rings, particularly for the Weyl group of symplectic groups Sp(n) and for the alternating groups A_n as the subgroup of W(SU(n)). We will ask if such rings of invariants are polynomial rings, and if each of them can be realized as the mod p cohomology of a space. For n = 3, 4, the rings under a conjugate of W(Sp(n)) are shown to be polynomial, and for n = 6, 8, they are non-polynomial. The structures of H*(BT^n-1; 𝔽_p)^A_n will be also discussed for n = 3, 4.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.691-699
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• 1997

The following statement is known as the generalized Hilbert-Smith conjecture : If G is a compact group and acts effectively on a manifold, then G is a Lie group. In this paper we prove that the generalized Hilbert-Smith conjecture is equivalent to the following : A known, but has never been published before.