• 대한수학회보
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• 제61권3호
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• pp.785-796
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• 2024

Let p be a prime. A group G is said to be residually p-finite if for each non-trivial element x of G, there exists a normal subgroup N of index a power of p in G such that x is not in N. In this note we shall prove that certain HNN extensions of free abelian groups of finite rank are residually p-finite. In addition some of these HNN extensions are subgroup separable. Characterisations for certain one-relator groups and similar groups including the Baumslag-Solitar groups to be residually p-finite are proved.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제14권2호
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• pp.154-161
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• 2014

We discuss some interesting sublattices of interval-valued fuzzy subgroups. In our main result, we consider the set of all interval-valued fuzzy normal subgroups with finite range that attain the same value at the identity element of the group. We then prove that this set forms a modular sublattice of the lattice of interval-valued fuzzy subgroups. In fact, this is an interval-valued fuzzy version of a well-known result from classical lattice theory. Finally, we employ a lattice diagram to exhibit the interrelationship among these sublattices.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.945-959
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• 2008

n-ary $H_v$-structures is a generalisation of both n-ary structures and $H_v$-structures. A wide class of n-ary $P-H_v$-groups is the n-ary $P-H_v$-groups that is concidered in this paper. In this paper the notion of a normal subgroup of an n-ary $P-H_v$-groups is introduced and the isomorphism theorems for n-ary $P-H_v$-groups are stated and proved. Also some examples and related properties are investigated.

• 호남수학학술지
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• 제26권4호
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• pp.559-587
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• 2004

We study some properties of intuitionistic fuzzy normal subgroups of a group. In particular, we obtain two characterizations of intuitionistic fuzzy normal subgroups. Moreover, we introduce the concept of an intuitionistic fuzzy coset and obtain several results which are analogous of some basic theorems of group theory.

• Kyungpook Mathematical Journal
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• 제63권2호
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• pp.187-198
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• 2023

The motivation for this study comes from a question posed by I.N. Herstein in the Israel Journal of Mathematics in 1978. Specifically, let D be a division ring with center F. The aim of this paper is to demonstrate that every quasinormal subgroup of the multiplicative group of D, which is radical over some proper division subring, is central if one of the following conditions holds: (i) D is weakly locally finite; (ii) F is uncountable; or (iii) D is the Mal'cev-Neumann division ring.

• Journal of Gastric Cancer
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• 제18권3호
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• pp.274-286
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• 2018

Purpose: The aim of this study was to investigate the impact of preoperative low body mass index (BMI) on both the short- and long-term outcomes in patients with gastric cancer. Materials and Methods: A total of 510 patients with gastric cancer were divided into the following 3 groups: low BMI group (${\leq}18.5kg/m^2$, n=51), normal BMI group ($18.6-24.9kg/m^2$, n=308), and high BMI group (${\geq}25.0kg/m^2$, n=151). Results: There were significantly more stage III/IV patients in the low BMI group than in the other groups (P=0.001). Severe postoperative complications were more frequent (P=0.010) and the survival was worse (P<0.001) in the low BMI group. The subgroup analysis indicated that survival was worse in the low BMI group of the stage I/II subgroup (P=0.008). The severe postoperative complication rate was higher in the low BMI group of the stage III/IV subgroup (P=0.001), although the recurrence rate and survival did not differ in the stage III/IV subgroup among all the BMI groups. Low BMI was an independent poor prognostic factor in the stage I/II subgroup (disease-free survival: hazard ratio [HR], 13.521; 95% confidence interval [CI], 1.186-154.197; P=0.036 and overall survival: HR, 5.130; 95% CI, 1.644-16.010; P=0.005), whereas low BMI was an independent risk factor for severe postoperative complications in the stage III/IV subgroup (HR, 17.158; 95% CI, 1.383-212.940; P=0.027). Conclusions: Preoperative low BMI in patients with gastric cancer adversely affects survival among those with stage I/II disease and increases the severe postoperative complication rate among those with stage III/IV disease.

• Kyungpook Mathematical Journal
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• 제62권4호
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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 p^rm 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 p^rm is solvable for all r, and we obtain the value of r₀ for a case where m is a product of two primes.

• 대한수학회논문집
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• 제11권3호
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• pp.797-805
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• 1996

We provide a new proof of the following fact using least area surfaces : If the fundamental group of a $P^2$-irreducible closed 3-manifold M contains a finitely generated nontrivial normal subgroup of infinite index, then M has a finite cover which is a closed surface bundle over $S^1$ , unless N is free.

• 대한수학회지
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• 제32권3호
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• pp.371-387
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• 1995

Let X be a compact polyhedron, H a normal subgroup of the fundamental group $\pi_1(X)$ of X and $f : X \longrightarrow X$ a selfmap such that $f_piH \subset H$, where f_\pi : \pi_1(X) \longrightarrow \pi_1(X)$ is the induced homomorphism by f.

• 대한수학회보
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• 제40권2호
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• pp.177-182
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• 2003

A metacyclic group is a group that has a cyclic normal subgroup with cyclic quotient. We characterize finite metacyclic groups that have faithful irreducible representations over a given field.