• Title, Summary, Keyword: finite group

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FINITE GROUPS WITH A CYCLIC NORM QUOTIENT

  • Wang, Junxin
    • 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.

FREE ACTIONS OF FINITE GROUPS ON 3-DIMENSIONAL NILMANIFOLDS WITH HOMOTOPICALLY TRIVIAL TRANSLATIONS

  • Koo, Daehwan;Park, Eunmi;Shin, Joonkook
    • Journal of the Chungcheong Mathematical Society
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    • v.33 no.1
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    • pp.113-132
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    • 2020
  • We show that if a finite group G acts freely with homotopically trivial translations on a 3-dimensional nilmanifold 𝓝p with the first homology ℤ2 ⊕ ℤp, then either G is cyclic or there exist finite nonabelian groups acting freely on 𝓝p which yield orbit manifolds homeomorphic to 𝓝/𝜋3 or 𝓝/𝜋4.

THE GROUP OF UNITS OF SOME FINITE LOCAL RINGS II

  • Woo, Sung-Sik
    • Journal of the Korean Mathematical Society
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    • v.46 no.3
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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.

ERGODICITY AND RANDOM WALKS ON A COMPACT GROUP

  • CHOE, GEON HO
    • 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.

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Mechanical Response of Changes in Design of Compression Hip Screws with Biomechanical Analysis (생체 역학적 분석에 의한 Compression Hip Screw의 디자인 요소에 대한 평가)

  • 문수정;이희성;권순영;이성재;안세영;이훈
    • Proceedings of the Korean Society of Precision Engineering Conference
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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.

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STRUCTURE OF SOME CLASSES OF SEMISIMPLE GROUP ALGEBRAS OVER FINITE FIELDS

  • Makhijani, Neha;Sharma, Rajendra Kumar;Srivastava, J.B.
    • 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.

A FINITE PRESENTATION FOR THE TWIST SUBGROUP OF THE MAPPING CLASS GROUP OF A NONORIENTABLE SURFACE

  • Stukow, Michal
    • 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.

MINIMAL DEL PEZZO SURFACES OF DEGREE 2 OVER FINITE FIELDS

  • Trepalin, Andrey
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.5
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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.

CLASSIFICATION OF FREE ACTIONS OF FINITE GROUPS ON 3-DIMENSIONAL NILMANIFOLDS

  • Koo, Daehwan;Oh, Myungsung;Shin, Joonkook
    • 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.