• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.779-783
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• 2004

A group G is said to satisfy the minimal condition on normal subgroups of infinite index if there does not exist an infinite properly descending chain $G_1$ > $G_2$ > ... of normal subgroups of infinite index in G. We characterize the structure of locally nilpotent groups satisfying this chain condition.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1063-1073
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• 2014

A finite group G is called a $\mathcal{QNS}$-group if every minimal subgroup X of G is either quasinormal in G or self-normalizing. In this paper the authors classify the non-$\mathcal{QNS}$-groups whose proper subgroups are all $\mathcal{QNS}$-groups.

• Journal of the Korean Institute of Intelligent Systems
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• v.8 no.6
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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.

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.105-109
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• 2008

We study the structure of metanilpotent groups satisfying the maximal condition on infinite normal subgroups or the minimal condition on normal subgroups of infinite index.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.763-769
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• 2007

We study the structure of abelian-by-nilpotent groups satisfying the maximal condition on infinite normal subgroups or the minimal condition on normal subgroups of infinite index.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.687-691
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• 2010

In this article we will prove that a generalized radical group satisfying the maximal condition for subnormal subgroups of infinite order (the minimal condition for subnormal subgroups of infinite index, respectively) is soluble-by-finite. Such result generalizes that obtained by D. H. Paek in [5].

• Journal of the Korean Mathematical Society
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• v.56 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2079-2087
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• 2013

An $\mathcal{SQNS}$-group G is a group in which every proper subgroup of G is either s-quasinormal or self-normalizing and a minimal non-$\mathcal{SQNS}$-group is a group which is not an $\mathcal{SQNS}$-group but all of whose proper subgroups are $\mathcal{SQNS}$-groups. In this note all the finite minimal non-$\mathcal{SQNS}$-groups are determined.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.03a
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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.