• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.465-472
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• 2004

A group G is said to satisfy the maximal condition on infinite normal subgroups if there does not exist an infinite properly ascending chain of infinite normal subgroups. We characterize the structure of locally nilpotent groups satisfying this chain condition. We then show how to construct locally nilpotent groups with the maximal condition on infinite normal subgroups, but not the maximal condition on subgroups.

• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.805-819
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• 2022

We describe the structure of finite p-groups in which all normal closures of non-normal subgroups have two orders for p > 2.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.719-727
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• 2022

In this paper, the concept of (𝛾, 𝜕)-fuzzy HX-subgroups is introduced. We present some properties of (𝛾, 𝜕)-normal fuzzy HX-subgroups and we discuss some results related to (𝛾, 𝜕)-fuzzy cosets.

• 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.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.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1165-1178
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• 2009

In this paper we classify finite groups whose nonnormal subgroups are of order p or pq, where p, q are primes. As a by-product, we also classify the finite groups in which all nonnormal subgroups are cyclic.

• Honam Mathematical Journal
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• v.26 no.4
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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.

• Honam Mathematical Journal
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• v.28 no.1
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• pp.31-44
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• 2006

We discuss various types of sublattice of the lattice of intuitionistic fuzzy subgroups of a given group. We prove that a special class of intuitionitic fuzzy normal subgroups constitutes a modular sublattice of the lattice of intuitionistic fuzzy subgroups.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.665-677
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• 2005

The notion of normal intuitionistic fuzzy R-subgroups in near-rings is introduced, and related properties are investigated. Characterization of an intuitionistic fuzzy R-subgroup is given. Using a collection of right R-subgroups, an intuitionistic fuzzy right R-subgroup is established. Using a chain of right R-subgroups, an intuitionistic fuzzy right R-subgroup is also established.