• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.479-486
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• 2016

The norm N(G) of a group G is the intersection of the normalizers of all the subgroups of G. In this paper, the structure of finite groups with a cyclic norm quotient is determined. As an application of the result, an interesting characteristic of cyclic groups is given, which asserts that a finite group G is cyclic if and only if Aut(G)/P(G) is cyclic, where P(G) is the power automorphism group of G.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.25-33
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• 2001

Let G be a finite group with a probability measure. We investigate the random walks on G in terms of ergodicity of the associated skew product transformation.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.765-767
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• 2022

The inverse Galois problem concerns whether or not every finite group appears as the Galois group of some Galois extension of the rational numbers. This problem, first posed in the early 19th century, is unsolved. In other words, we consider a pair - the group G and the field K. The question is whether there is an extension field L of K such that G is the Galois group of L. In this paper we present the proof that any group G is a Galois group of any field extension. In other words, we only consider the group G. And we present the solution to the inverse Galois problem.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.1172-1175
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• 2004

At present, CHS(Compression Hip Screw) is one of the best prosthesis for the intertrochanteric fracture. There is nothing to evaluate the CHS itself with the finite element analysis and mechanical tests. They have same ways of the experimental test of the ASTM standards. The purpose of this study is to evaluate the existing CHS and the new CHS which have transformational design factors with finite element analysis and mechanical tests. The mechanical tests are divided into compression tests and fatigue test for evaluating the failure load, strength and fatigue life. This finite element method is same as the experimental test of the ASTM standards. Under 300N of compression load at the lag screw head. There are less differences between Group (5H, basic type) and Group which has 8 screw holes. However, there are lots of big differences between Group and Group which is reinforced about thickness of the neck range. Moreover, the comparison of Group and Group shows similar tendency of the comparison of Group and Group . The Group is reinforced the neck range from Group. After the experimental tests and the finite element analysis, the most effective design factor of the compression hip screws is the reinforcement of the thickness, even though, there are lots of design factors. Moreover, to unite the lag screw with the plate and to analyze by static analysis, the result of this method can be used with experimental test or instead of it.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.697-704
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• 2013

The function $g{\mapsto}{\zeta}^k_G(g)$ which counts the number of solutions of $x^k=g$ in a finite group G, is not necessarily a character of G. We study this function for the case of dihedral groups and generalized quaternion groups.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1605-1614
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• 2014

In continuation to the investigation initiated by Ferraz, Goodaire and Milies in [4], we provide an explicit description for the Wedderburn decomposition of finite semisimple group algebras of the class of finite groups G, such that $$G/Z(G){\simeq_-}C_2{\times}C_2$$, where Z(G) denotes the center of G.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.889-897
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• 2001

Based on the prime graph of a finite simple group, its order is the product of its order components (see[4]). It is known that Suzuki-Ree groups [6], $PSL_2(q)$ [8] and $E_8(q)$ [7] are uniquely deternubed by their order components. In this paper we prove that the simple groups $A_p$ are also unipuely determined by their order components, where p and p-2 are primes.

• Journal of the Korean Mathematical Society
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• v.46 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1411-1440
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• 2017

We study free actions of finite groups on 3-dimensional nil-manifolds with the first homology ${\mathbb{Z}}^2{\oplus}{\mathbb{Z}}_p$. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal nilpotent subgroups of almost Bieberbach groups of finite index, up to affine conjugacy.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.601-614
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• 2016

Let $N_{g,s}$ denote the nonorientable surface of genus g with s boundary components. Recently Paris and Szepietowski [12] obtained an explicit finite presentation for the mapping class group $\mathcal{M}(N_{g,s})$ of the surface $N_{g,s}$, where $s{\in}\{0,1\}$ and g + s > 3. Following this work, we obtain a finite presentation for the subgroup $\mathcal{T}(N_{g,s})$ of $\mathcal{M}(N_{g,s})$ generated by Dehn twists.