• 대한수학회지
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• 제56권3호
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• pp.739-750
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• 2019

We proved that finite p-groups in the title coincide with finite p-groups all of whose non-abelian subgroups are generated by two elements. Based on the result, finite p-groups all of whose subgroups of class 2 are minimal non-abelian (of the same order) are classified, respectively. Thus two questions posed by Berkovich are solved.

• 충청수학회지
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• 제12권1호
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• pp.163-168
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• 1999

In this paper we discuss another normalization of fuzzy R-subgroups in near-rings.

• 대한수학회지
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• 제49권1호
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• pp.201-221
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• 2012

Assume G is a finite p-group and i is a fixed positive integer. In this paper, finite p-groups G with ${\mid}N_G(H):H{\mid}=p^i$ for all nonnormal subgroups H are classified up to isomorphism. As a corollary, this answer Problem 116(i) proposed by Y. Berkovich in his book "Groups of Prime Power Order Vol. I" in 2008.

• 대한수학회지
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• 제29권1호
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• pp.1-8
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• 1992

• 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.

• 호남수학학술지
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• 제32권4호
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• pp.593-617
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• 2010

We introduce the concepts of interval-valued fuzzy sub-groups [resp. normal subgroups, rings and ideals] and investigate some of it's properties.

• 호남수학학술지
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• 제32권4호
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• pp.545-561
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• 2010

We introduce the concepts of interval-valued fuzzy sub-groups [resp. normal subgroups, rings and ideals] and investigate some of it's properties.

• Korean Journal of Mathematics
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• 제26권3호
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• pp.373-385
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• 2018

In this paper we introduce the notion of a fuzzy kernel of a fuzzy homomorphism on groups and we show that it is a fuzzy normal subgroup of the domain group. Conversely, we also prove that any fuzzy normal subgroup is a fuzzy kernel of some fuzzy epimorphism, namely the canonical fuzzy epimorphism. Finally, we formulate and prove the fuzzy version of the fundamental theorem of homomorphism and those isomorphism theorems.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2004년도 춘계학술대회 학술발표 논문집 제14권 제1호
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• pp.367-371
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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 analogs of some basic theorems of group theory.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제12권3호
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• pp.205-214
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• 2012

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