• 대한수학회보
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• 제54권5호
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• pp.1779-1801
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• 2017

Let X be a minimal del Pezzo surface of degree 2 over a finite field ${\mathbb{F}}_q$. The image ${\Gamma}$ of the Galois group Gal(${\bar{\mathbb{F}}}_q/{\mathbb{F}}_q$) in the group Aut($Pic({\bar{X}})$) is a cyclic subgroup of the Weyl group W($E_7$). There are 60 conjugacy classes of cyclic subgroups in W($E_7$) and 18 of them correspond to minimal del Pezzo surfaces. In this paper we study which possibilities of these subgroups for minimal del Pezzo surfaces of degree 2 can be achieved for given q.

• 대한수학회논문집
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• 제25권1호
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• pp.111-117
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• 2010

For a based, 1-connected, finite CW-complex X, we denote by $\varepsilon(X)$ the group of homotopy classes of self-homotopy equivalences of X and by $\varepsilon_#\;^{dim+r}(X)$ the subgroup of homotopy classes which induce the identity on the homotopy groups of X in dimensions $\leq$ dim X+r. In this paper, we calculate the subgroups $\varepsilon_#\;^{dim+r}(X)$ when X is a wedge of two Moore spaces determined by cyclic groups and in consecutive dimensions.

• 대한수학회지
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• 제45권6호
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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.

• 대한수학회보
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• 제44권1호
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• pp.61-71
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• 2007

A group G is called cyclic subgroup separable for the cyclic subgroup H if for each $x\;{\in}\;G{\backslash}H$, there exists a normal subgroup N of finite index in G such that $x\;{\not\in}\;HN$. Clearly a cyclic subgroup separable group is residually finite. In this note we show that certain polygonal products of cyclic subgroup separable groups amalgamating normal subgroups are again cyclic subgroup separable. We then apply our results to polygonal products of polycyclic-by-finite groups and free-by-finite groups.

• 대한수학회논문집
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• 제12권3호
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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.

• 대한수학회보
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• 제48권6호
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• pp.1147-1155
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• 2011

In J. Korean Math. Soc, Zhang, Xu and other authors investigated the following problem: what is the structure of finite groups which have many normal subgroups? In this paper, we shall study this question in a more general way. For a finite group G, we define the subgroup $\mathcal{A}(G)$ to be intersection of the normalizers of all non-cyclic subgroups of G. Set $\mathcal{A}_0=1$. Define $\mathcal{A}_{i+1}(G)/\mathcal{A}_i(G)=\mathcal{A}(G/\mathcal{A}_i(G))$ for $i{\geq}1$. By $\mathcal{A}_{\infty}(G)$ denote the terminal term of the ascending series. It is proved that if $G=\mathcal{A}_{\infty}(G)$, then the derived subgroup G' is nilpotent. Furthermore, if all elements of prime order or order 4 of G are in $\mathcal{A}(G)$, then G' is also nilpotent.

• The Journal of Advanced Prosthodontics
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• 제11권5호
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• pp.253-261
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• 2019

PURPOSE. To evaluate the influence of cyclic loading on phase transformation of zirconia abutments and to compare the effectiveness of three different quantitative ageing assessment techniques. MATERIALS AND METHODS. Thirty two Y-TZP prostheses fabricated from two brands, InCoris ZI and Ceramill ZI, were cemented to titanium bases and equally divided into two subgroups (n=8): control group without any treatment and aged group with cyclic loading between 20 N and 98 N for 100,000 cycles at 4 Hz in distilled water at $37^{\circ}C$. The tetragonal-to-monoclinic phase transformation was assessed by (i) conventional x-ray diffraction (XRD), (ii) micro x-ray diffraction (${\mu}XRD$), and (iii) micro-Raman spectroscopy. The monoclinic-phase fractions (M%) were compared by two-way ANOVA. RESULTS. InCoris Zi presented significantly higher M% than Ceramill Zi in both control and aged groups (P<.001). Both materials exhibited significant phase transformation with monoclinicphase of 1 to 3% more in aged groups than controls for all three assessment techniques. The comparable M% was quantified by both ${\mu}XRD$ and XRD. The highest M% was assessed with micro-Raman. CONCLUSION. Cyclic loading produced significant phase transformation in tested Y-TZP prostheses. The micro-Raman spectroscopy could be used as an alternative to XRD and ${\mu}XRD$.

• Korean Journal of Mathematics
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• 제22권3호
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• pp.501-516
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• 2014

We define the class of almost ${\omega}_1-p^{\omega+n}$-projective abelian p-primary groups and investigate their basic properties. The established results extend classical achievements due to Hill (Comment. Math. Univ. Carol., 1995), Hill-Ullery (Czech. Math. J., 1996) and Keef (J. Alg. Numb. Th. Acad., 2010).

• 대한수학회지
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• 제46권3호
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• pp.475-491
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• 2009

In [2], we identified the group of units of finite local rings $\mathbb{Z}_4[X]$/($X^k+2X^a$, $2X^r$) with certain restrictions on a. In this paper we find direct sum decomposition of the group of units of such rings without restrictions on a into cyclic subgroups by finding their generators. And further generalization is considered.

• 대한수학회지
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• 제46권2호
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• pp.295-311
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• 2009

The purpose of this paper is to identify the group of units of finite local rings of the types ${\mathbb{F}}_2[X]/(X^k)$ and ${\mathbb{Z}}_4[X]/I$, where I is an ideal. It turns out that they are 2-groups and we give explicit direct sum decomposition into cyclic subgroups of 2-power order and their generators.