• Title/Summary/Keyword: normal subgroups

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A note on M-groups

  • 왕문옥
    • Journal for History of Mathematics
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    • v.12 no.2
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    • pp.143-149
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    • 1999
  • Every finite solvable group is only a subgroup of an M-groups and all M-groups are solvable. Supersolvable group is an M-groups and also subgroups of solvable or supersolvable groups are solvable or supersolvable. But a subgroup of an M-groups need not be an M-groups . It has been studied that whether a normal subgroup or Hall subgroup of an M-groups is an M-groups or not. In this note, we investigate some historical research background on the M-groups and also we give some conditions that a normal subgroup of an M-groups is an M-groups and show that a solvable group is an M-group.

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SUBPERMUTABLE SUBGROUPS OF SKEW LINEAR GROUPS AND UNIT GROUPS OF REAL GROUP ALGEBRAS

  • Le, Qui Danh;Nguyen, Trung Nghia;Nguyen, Kim Ngoc
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.1
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    • pp.225-234
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    • 2021
  • Let D be a division ring and n > 1 be an integer. In this paper, it is shown that if D ≠ ��3, then every subpermutable subgroup of the general skew linear group GLn(D) is normal. By applying this result, we show that every subpermutable subgroup of the unit group (ℝG)∗ of the real group algebras RG of finite groups G is normal in (ℝG)∗.

Group Orders That Imply a Nontrivial p-Core

  • Rafael, Villarroel-Flores
    • Kyungpook Mathematical Journal
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    • v.62 no.4
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    • pp.769-772
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    • 2022
  • Given a prime number p and a natural number m not divisible by p, we propose the problem of finding the smallest number r0 such that for r ≥ r0, every group G of order prm has a non-trivial normal p-subgroup. We prove that we can explicitly calculate the number r0 in the case where every group of order prm is solvable for all r, and we obtain the value of r0 for a case where m is a product of two primes.

FREE ACTIONS ON THE NILMANIFOLD

  • Shin, Joonkook
    • Journal of the Chungcheong Mathematical Society
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    • v.10 no.1
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    • pp.161-175
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    • 1997
  • We classify free actions of finite abelian groups on the 3-dimensional nilmanifold, up to topological conjugacy. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal subgroups of almost Bieberbach groups of finite index, up to affine conjugacy.

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TL-FINITE STATE MACHINES OVER FINITE GROUPS

  • Cho, Sung-Jin
    • Journal of applied mathematics & informatics
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    • v.8 no.3
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    • pp.1009-1019
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    • 2001
  • We introduce the concepts of TL-finite state machine, TL-kernel and TL-subfinite state machines, TL-kernel and TL-subfinite state machine and obtain some results concerning them.

COMMUTATOR LENGTH OF SOLVABLE GROUPS SATISFYING MAX-N

  • Mehri, Akhavan-Malayeri
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.4
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    • pp.805-812
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    • 2006
  • In this paper we find a suitable bound for the number of commutators which is required to express every element of the derived group of a solvable group satisfying the maximal condition for normal subgroups. The precise formulas for expressing every element of the derived group to the minimal number of commutators are given.

Comparison of Cardiovascular Risk Profile Clusters Among Industrial Workers

  • Hwang, Seon-Young;Lee, Ji-Hyun
    • Journal of Korean Academy of Nursing
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    • v.35 no.8
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    • pp.1500-1507
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    • 2005
  • Purpose. The purpose of this study was to identify subgroups of the physical and behavioral risk profiles for cardiovascular disease among industrial workers, and to examine predicting factors for the subgroups. Sample and Method. Health records of 2,616 male and female workers aged 19-56 years who were employed in an airplane manufacturing industry were analyzed. Data were analyzed using the Latent class cluster analysis. Results. Four different clusters (two high-risk groups, one low-risk group, and one normal group) were found and these clusters were significantly different by age, gender, and work type (p < .05 ). The two high-risk groups had higher chances of drinking alcohol, elevated BMI, FBS, total cholesterol, having hypertension, and were significantly older, and had relatively high chances of being day workers rather than other groups. The low-risk group had higher chances of drinking alcohol, higher BMI and total cholesterols compared to normal group, and highest portions of current smokers and shift workers in the four clusters and their mean BP was within prehypertension criteria. Conclusion. Industrial nurses should guide the lifestyle behaviors and risk factors of the high risk groups for CVD and need to intervene early for behavioral change for the low-risk group who are young and shift workers. Age, and work environment should be considered in planning for targeted preventive interventions for industrial workers.

Associations Between Age, Cytogenetics, FLT3-ITD, and Marrow Leukemia Cells Identified by Flow Cytometry

  • Su, Long;Gao, Su-Jun;Tan, Ye-Hui;Han, Wei;Li, Wei
    • Asian Pacific Journal of Cancer Prevention
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    • v.14 no.9
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    • pp.5341-5344
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    • 2013
  • Objectives: To explore the relationships between age, cytogenetic subgroups, molecular markers, and cells with leukemic aberrant immunophenotype in patients with acute myeloid leukemia (AML). Methods: In this study, we evaluated the correlations between age, cytogenetic subgroups (normal, balanced and unbalance karyotype), molecular mutations (NPM1, FLT3-ITD, and CEBPA mutations) and marrow leukemia cells (LC) identified by flow cytometry in 256 patients with de novo AML. Results: From age group 10-19 years to age group ${\geq}60$ years, the percentage of LC decreased from $67.0{\pm}18.4%$ to $49.0{\pm}25.1%$ (F=2.353, P=0.041). LC percentage was higher in patients with balanced karyotypes ($65.7{\pm}22.4%$), than those with unbalanced karyotypes ($46.0{\pm}26.6%$) (u=3.444, P=0.001) or a normal karyotype ($49.9{\pm}22.1%$) (u=5.093, P<0.001). Patients with FLT3-ITD ($64.3{\pm}19.5%$) had higher LC percentages compared with those without ($54.2{\pm}24.3%$) (u=2.794, P=0.007). Conclusions: Associations between age, cytogenetics, molecular markers, and marrow leukemia cells may offer beneficial information to understand the biology and pathogenesis of AML.

Survey on Food Consumption Patterns and Nutrient Intakes of College Students by Body Mass Index (체질량지수에 따른 남녀대학생들의 식품 소비경향과 영양소 섭취실태에 관한 연구)

  • Choi, Ji-Hyun;Wang, Soo-Kyung
    • Journal of the Korean Society of Food Culture
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    • v.11 no.5
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    • pp.689-698
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    • 1996
  • This study was designed to investigate food consumption patterns and nutrient intakes of college students, divided into subgroups of normal weight men (no.=140), normal weight women (no.=101), and underweight women (no.=155) by body mass index. Frequency of food eaten, nutrient intakes from each meal, percentages of RDAs, and nutrient densities were analyzed using 24-hour recall records. It was very interesting in these results as follows. Normal weight men ate on the whole more frequently than other groups. Underweight women had higher intakes of nutrient than did normal weight women. However normal weight women consumed food of greater nutrient density than did other college students. Consequently, it is desirable to suggest nutrient density of food than learn RDAs for adequate diet in nutritional education programs.

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