Nilpotent fuzzy subgroups
type: Item
instance of: scholarly article
title: Nilpotent fuzzy subgroups
zbMATH Open document ID: 1402.20071
author: Elaheh Mohammadzadeh
author: R. A. Borzooei
published in: Mathematics
publication date: 2018-08-13T00:00:00Z
review text: Summary: In this paper, we introduce a new definition for nilpotent fuzzy subgroups, which is called the good nilpotent fuzzy subgroup or briefly g-nilpotent fuzzy subgroup. In fact, we prove that this definition is a good generalization of abstract nilpotent groups. For this, we show that a group \(G\) is nilpotent if and only if any fuzzy subgroup of \(G\) is a g-nilpotent fuzzy subgroup of \(G\). In particular, we construct a nilpotent group via a g-nilpotent fuzzy subgroup. Finally, we characterize the elements of any maximal normal abelian subgroup by using a g-nilpotent fuzzy subgroup.
Mathematics Subject Classification ID: 20N25
zbMATH DE Number: 6916901
zbMATH Keywords: nilpotent group
zbMATH Keywords: nilpotent fuzzy subgroup
zbMATH Keywords: generalized nilpotent fuzzy subgroup
MaRDI profile type: Publication
full work available at URL: math6020027
OpenAlex ID: W2792396669
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Wikidata QID: Q130206782
DOI: 10.3390/MATH6020027
description: scientific article; zbMATH DE number 6916901