• Title/Summary/Keyword: group extension

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THE INVERSE GALOIS PROBLEM

  • MATYSIAK, LUKASZ
    • 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.

FINITE EXTENSIONS OF WEIGHTED WORD L-DELTA GROUPS

  • Ryang, Do-Hyoung
    • The Pure and Applied Mathematics
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    • v.15 no.4
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    • pp.353-364
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    • 2008
  • The purpose of this paper is to investigate the finite extension of weighted word L-delta groups. The paper revealed that a finite extension of a weighted word L-delta group is a weighted word L-delta group, and an abelian group, in addition, is a weighted word L-delta group and simultaneously a word L-delta group.

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ON GROUP EXTENSIONS OF MINIMAL HOMEOMORPHISMS II

  • Kim, Young-Key
    • Communications of the Korean Mathematical Society
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    • v.10 no.2
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    • pp.393-400
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    • 1995
  • We define a group extension and characterized some properties of the group extension. In particular, we show that the quotient map $\nu$ is a continuous group isomorphism and subgroup $H_1(H_2)$ is normal in $G_1(G_2)$.

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The comparison about lumbar extensor strength between pre op group and post op(after 6 weeks) group in HIVD patient (만성요통환자의 레이져 수술전과 수술6주후의 요부신전근력에 관한 비교)

  • Park, Sung-Kwang;Sok, Hye-Kyong;Kim, Myung-Joon
    • Journal of Korean Physical Therapy Science
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    • v.7 no.1
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    • pp.353-365
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    • 2000
  • The purpose of this study were to compare the lumbar extensor strength between pre op patients group and after 6 weeks post op patients group. To evaluate lumbar extensor strength of total 273 patients with HIVD. Lumbar extensor strength was measured in 151 male patients and 122 female patients(Lumbar extensor strength was measured in 91 PELD patients group and 182 OLM group patients) by Medx lumbar extension machine. Maximum voluntary lumbar extension strength was appear $149.36{\pm}61.92ft$-lbs in pre op of PELD group, $158.47{\pm}54.67ft$-lbs in post op of PELD group and $135.54{\pm}54.24ft$-lbs in pre op of OLM group. $147.19{\pm}52.42ft$-lbs in post op of OLM group in male. Maximum voluntary lumbar extension strength was appear $83.85{\pm}30.22ft$-lbs in pre op of PELD group. $92.99{\pm}28.66ft$-lbs in post op of PELD group and $75.16{\pm}24.98ft$-lbs in pre op of OLM group, $79.88{\pm}25.25ft$-lbs in post op of OLM group in female. Male and female lumbar extension strength was statistically significant difference(P<.05). Lumbar flexion/extension ratio of the two group was 2.14:1 pre op and 2.05:1 post op in lumbar flexion 72 and 0 degree. The ratio of post op group was lesser than pre op group.

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The Immediate Effect of Hip Flexor Stretching with Pelvic Fixation on Hip Extension Flexibility and Gait Parameters in Subjects with Unilateral Hip flexor Shortness (골반 고정을 동반한 엉덩관절 굽힘근 스트레칭이 일측성 엉덩관절 굽힘근 단축이 있는 일반 성인의 엉덩관절 폄 유연성과 보행 매개변수에 미치는 즉각적인 효과)

  • Kim, Tae-Gyu;Kim, Young-Hoon;Kim, Soo-Yong
    • PNF and Movement
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    • v.20 no.1
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    • pp.83-90
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    • 2022
  • Purpose: The purpose of this study was to investigate the immediate effects of hip flexor stretching with pelvic fixation on the flexibility of hip extension and gait capacity in subjects with limited hip extension flexibility. Methods: Twenty-six subjects with limited hip extension flexibility were divided into two groups: a hip flexor stretching with pelvic fixation group (n = 13) and a hip flexor stretching without pelvic fixation group (n = 13). The subjects were assessed based on flexibility of hip extension, stride, and gait velocity after applying hip flexor stretching. Results: The hip flexor stretching with pelvic fixation group showed significantly improved flexibility of hip extension, stride, and gait velocity compared with hip flexor stretching without pelvic fixation group (p <0.05). The flexibility of hip extension was significantly improved after application of hip flexor stretching in both groups; however, stride and gait velocity were significantly improved only in the hip flexor stretching with pelvic fixation group. Conclusion: Hip flexor stretching with pelvic fixation is an effective intervention for improving the flexibility of hip extension and gait capacity.

COHOMOLOGY GROUPS OF RADICAL EXTENSIONS

  • Choi, Eun-Mi
    • Journal of the Korean Mathematical Society
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    • v.44 no.1
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    • pp.151-167
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    • 2007
  • If k is a subfield of $\mathbb{Q}(\varepsilon_m)$ then the cohomology group $H^2(k(\varepsilon_n)/k)$ is isomorphic to $H^2(k(\varepsilon_{n'})/k)$ with gcd(m, n') = 1. This enables us to reduce a cyclotomic k-algebra over $k(\varepsilon_n)$ to the one over $k(\varepsilon_{n'})$. A radical extension in projective Schur algebra theory is regarded as an analog of cyclotomic extension in Schur algebra theory. We will study a reduction of cohomology group of radical extension and show that a Galois cohomology group of a radical extension is isomorphic to that of a certain subextension of radical extension. We then draw a cohomological characterization of radical group.

The Effect of Trunk Extension Strengthening Exercise on Muscle Performance of Upper Limb in Adolescent Baseball Player (체간 신전근 강화훈련이 청소년기 야구선수의 상지 근수행력에 미치는 영향)

  • Choi, Joe-Haeng;Park, Jong-Hang
    • Journal of Korean Physical Therapy Science
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    • v.9 no.1
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    • pp.61-68
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    • 2002
  • The purpose of this dissertation was to analyze the effect of trunk extension strengthening exercise on muscle performance of the upper limb in adolescent baseball player. The twenty people were studied : experimental group(10), comparative group(10). The experimental group has done trunk extension strengthening exercise for 8 weeks. The study analyzes isometric maximal strength of shoulder internal rotation. shoulder external rotation, elbow flexion, elbow extension, forearm pronation, forearm supination and ball speed. All of subjects were tested for 3 times ; pre, mid, post. The results were as follows; 1. Maximal isometric strength of upper limb, during trunk extension strengthening exercise in experimental group, shoulder internal rotation and external rotation showed it has slightly increased and comparative group showed it has no change, but not significant elbow flexion and extension significantly(p<0.05) increased after exercise either for 4 or 8 weeks compared with that of control group. Forearm pronation showed not significantly changed in both group, but significantly different between group either for 4 or 8 weeks. Forearm supination, significantly((p<0.05) increased after 8 weeks in experimental group. 2. Ball speed showed slightly increased but not significantly in experimental group. These results it may expect improvement of upper limb muscle performance of upper limb in adolescent baseball player. However, in case of shoulder a point of view of bunk extension strengthening exercise of this study hasn't a significant influence. More experimental studies are needs, hereafter which will use more experimental subjects and various methods of exercise and new application of treatment term to define significant change.

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SCALAR EXTENSION OF SCHUR ALGEBRAS

  • Choi, Eun-Mi
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.3
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    • pp.453-467
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    • 2005
  • Let K be an algebraic number field. If k is the maximal cyclotomic subextension in K then the Schur K-group S(K) is obtained from the Schur k-group S(k) by scalar extension. In the paper we study projective Schur group PS(K) which is a generalization of Schur group, and prove that a projective Schur K-algebra is obtained by scalar extension of a projective Schur k-algebra where k is the maximal radical extension in K with mild condition.

A GALOIS EXTENSION WITH GALOIS GROUP DIHEDRAL GROUP OR GENERALIZED QUATERNION GROUP

  • Hwang, Yoon-Sung
    • Communications of the Korean Mathematical Society
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    • v.20 no.4
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    • pp.641-644
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    • 2005
  • Let L/F be a Galois quadratic extension such that F contains a primitive n-th root of 1. Let N = L(${\alpha}^{{\frac{1}{n}}$) where ${\alpha}{\in}L{\ast}$. We show that if $N_{L/F}({\alpha})\;{\in}L^n{\cap}F$, and [N : L] = m, then $G(N/ F) {\simeq}D_m$ or generalized quaternion group whether $N_{L/F}({\alpha})\;{\in}\;F^n\;or\;{\notin}F^n$, respectively.