A study of normal fuzzy subgroups and characteristic fuzzy subgroups of a fuzzy group |
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Authors: | Naseem Ajmal Iffat Jahan |
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Institution: | 1. Department of Mathematics, Zakir Hussain College, University of Delhi, J.L. Nehru Marg, New Delhi, 110006, India 2. Department of Mathematics, Ramjas College, University of Delhi, Delhi, 110007, India
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Abstract: | In this paper, we investigate the properties of normal fuzzy subgroups of a fuzzy group. We also introduce the notion of a characteristic fuzzy subgroup of a fuzzy group, of which we provide level subset and strong level subset characterizations. Then we prove that a characteristic fuzzy subgroup of a fuzzy group is a normal fuzzy subgroup. Besides we prove that the commutator subgroup generated by the commutator of two normal fuzzy subgroups of a fuzzy group is contained in their intersection. Finally, we construct many new lattices and sublattices of fuzzy subgroups and normal fuzzy subgroups of a given fuzzy group. We also construct lattices of characteristic fuzzy subgroups possessing sup-property. |
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