Nilpotent Fuzzy Subgroups

Elaheh Mohammadzadeh and Rajab Ali Borzooei
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Elaheh Mohammadzadeh: Department of Mathematics, Payame Noor University, Tehran 19395-3697, Iran
Rajab Ali Borzooei: Department of Mathematics, Shahid Beheshti University, G. C., Tehran 19395-3697, Iran

Mathematics, 2018, vol. 6, issue 2, 1-12

Abstract: 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.

Keywords: nilpotent group; nilpotent fuzzy subgroup; generalized nilpotent fuzzy subgroup (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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