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Nilpotent Fuzzy Subgroups

Author

Listed:
  • 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)

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.

Suggested Citation

  • Elaheh Mohammadzadeh & Rajab Ali Borzooei, 2018. "Nilpotent Fuzzy Subgroups," Mathematics, MDPI, vol. 6(2), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:2:p:27-:d:132390
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