On the Subgroups Lattice and Fuzzy Subgroups of Finite Groups U6n
In this paper, we treat accounting for the number of fuzzy (normal) subgroups of finite groups [Formula: see text]. In order to do this, we use the natural equivalence relation on the set of fuzzy (normal) subgroups of [Formula: see text], which has a consistent group theoretical foundation. In fact...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Tsinghua University Press
2022-04-01
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| Series: | Fuzzy Information and Engineering |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/16168658.2022.2119828 |
| Summary: | In this paper, we treat accounting for the number of fuzzy (normal) subgroups of finite groups [Formula: see text]. In order to do this, we use the natural equivalence relation on the set of fuzzy (normal) subgroups of [Formula: see text], which has a consistent group theoretical foundation. In fact, the corresponding equivalence classes of fuzzy (normal) subgroups of [Formula: see text] are closely connected to the structure of (normal) subgroups lattice of [Formula: see text] and chains of subgroups of [Formula: see text], which terminate in [Formula: see text]. In this regards, the Inclusion-Exclusion principle plays an essential role and in some situations leads to recurrence relations, whose their solutions can be easily found. |
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| ISSN: | 1616-8658 1616-8666 |