• 대한수학회논문집
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• 제34권4호
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• pp.1049-1067
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• 2019

In this paper, we discuss the number of distinct fuzzy subgroups of the group ${\mathbb{Z}}_{p^n}{\times}{\mathbb{Z}}_{q^m}{\times}{\mathbb{Z}}_r$, m = 1, 2, 3 where p, q, r are distinct primes for any $n{\in}{\mathbb{Z}}^+$ using the criss-cut method that was proposed by Murali and Makamba in their study of distinct fuzzy subgroups. The criss-cut method first establishes all the maximal chains of the subgroups of a group G and then counts the distinct fuzzy subgroups contributed by each chain. In this paper, all the formulae for calculating the number of these distinct fuzzy subgroups are given in polynomial form.

• Journal of applied mathematics & informatics
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• 제41권6호
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• pp.1237-1256
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• 2023

The tree products of groups with amalgamation subgroups are generalizations of the free products of groups with amalgamation subgroup. The aim of this paper is to construct a tree called the standard tree where the tree products of groups with amalgamation subgroups act without inversions and then find the quotient of this action. Furthermore, we show that if the amalgamation subgroups are finite and the factor groups act on disjoint trees then there exists a tree called the fiber tree where the tree products of groups with amalgamation subgroups act without inversions and find the quotients of this action. If each factor is a tree products with amalgamation subgroups, we get a new fiber tree and the corresponding factors.

• 한국지능시스템학회논문지
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• 제8권6호
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• pp.21-26
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• 1998

In this paper, we show that if a TL-subgroup can be written as the intersection of all its minimal TL-p-subgroups then some properties of the TL-subgroups characterize the properties of all its minimal TL-p-subgroups and investigate the properties of the join of a directed family of TL-subgroups.

• 대한수학회보
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• 제59권4호
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• pp.951-960
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• 2022

In this paper, we determine the finite p-group such that the intersection of its any two distinct minimal nonabelian subgroups is a maximal subgroup of the two minimal nonabelian subgroups, and the finite p-group in which any two distinct 𝓐₁-subgroups generate an 𝓐₂-subgroup. As a byproduct, we answer a problem proposed by Berkovich and Janko.

• 대한수학회보
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• 제35권4호
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• pp.719-726
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• 1998

In this paper, we consider conjugacy of subgroups of some split metacyclic groups of odd prime power order to determine the numbers of conjugacy classes of subgroups of those groups. The study was motivated by the linear isomorphism problem of metacyclic primitive linear groups.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 춘계학술대회 학술발표 논문집
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• pp.3-6
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• 1998

We introduce the notion of TL-p-subgroups that is an extension of the notion of fuzzy p-subgroups and show that a torsion TL-subgroup of an Abelian group with T=∧ can be written as the intersection of its minimal TL-p-subgroups.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1995년도 추계학술대회 학술발표 논문집
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• pp.335-337
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• 1995

The notion of Ap* of a fuzzy subgroup A is introduced. Using the notion, we characterize fuzzy subgroups and show that every commutative fuzzy subgroup characterized as the intersection of its all minimal fuzzy p*-subgroups.

• 한국수산과학회지
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• 제47권3호
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• pp.241-246
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• 2014

Viruses in the genus Megalocytivirus have been subdivided into four subgroups. Among these subgroups 2 and 4, represented by the red sea bream iridovirus (RBIV) and the olive flounder iridovirus (FLIV), respectively, are non-exotic. subgroups 1 and 3, represented by the red sea bream iridovirus (RSIV) and the infectious spleen and kidney necrosis virus (ISKNV), respectively, have not been detected in Korea and are known as exotic. Shellfish are filter-feeders, and can thus filter and accumulate Megalocytivirus in their digestive glands, allowing us to track viral contamination in surrounding aquatic environment. In this study, we developed a high-resolution melting (HRM) analysis to differentiate among subgroups of Megalocytivirus accumulated in shellfish, and confirmed the convenience and efficiency of this method. More than two subgroups of Megalocytivirus were found in the digestive gland of a single shellfish. We classified all Megalocytivirus viruses from shellfish in Korea into subgroups 2 and 4, although proportions of subgroups were different among regions. Compared to nucleotide sequencing analysis, HRM analysis is a simple and rapid method for differentiating of Megalocytivirus subgroups.

• 대한수학회논문집
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• 제28권1호
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• pp.55-62
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• 2013

In [5], Johnson introduced the primitivity of subgroups and proved that a finite group G is supersolvable if every primitive subgroup of G has a prime power index in G. In that paper, he also posed an interesting problem: what a group looks like if all of its primitive subgroups are maximal. In this note, we give the detail structure of such groups in solvable case. Finally, we use the primitivity of some subgroups to characterize T-group and the solvable $PST_0$-groups.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2004년도 춘계학술대회 학술발표 논문집 제14권 제1호
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• pp.389-393
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• 2004

In this paper, we introduce the concept of level subgroups of an intuitionistic fuzzy subgroup, and study some properties of level subgroups in the first part of the paper. These level subgroups in turn play an important role in the characterization of all intuitionistic fuzzy subgroups of a prime cyclic group.