- Title
- The classification of fuzzy subgroups of some finite non-cyclic abelian p- groups of rank 3, with emphasis on the number of distinct fuzzy subgroups
- Creator
- Appiah, Isaac Kwadwo
- Subject
- Fuzzy sets
- Subject
- Commutative algebra
- Date Issued
- 2021-03
- Date
- 2021-03
- Type
- Doctoral theses
- Type
- text
- Identifier
- http://hdl.handle.net/10353/20783
- Identifier
- vital:46563
- Description
- In [6] and [7] we classi_ed fuzzy subgroups of some rank-3 abelian groups of the form G = Zpn + Zp + Zp for any _xed prime integer p and any positive integer n, using the natural equivalence relation de_ned in [40]. In this thesis, we extend our classi_cation of fuzzy subgroups in [6] to the group G = Zpn + Zpm + Zp for any _xed prime integer p; m = 2 and any positive integer n using the same natural equivalence relation studied in [40]. We present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups of G for any n;m _ 2 and (iii) distinct fuzzy subgroups for m = 2 and n _ 2. We have also developed user-friendly polynomial formulae for the number of (iv) subgroups, (v) maximal chains for the group G = Zpn + Zpm for any n;m _ 2; any _xed prime positive integer p and (vi) distinct fuzzy subgroups of Zpn + Zpm for m equal to 2 and 3, and n _ 2 and provided their proofs.
- Description
- Thesis (PhD) -- Faculty of Science and Agriculture, 2021
- Format
- computer
- Format
- online resource
- Format
- application/pdf
- Format
- 1 online resource (255 pages)
- Format
- Publisher
- University of Fort Hare
- Publisher
- Faculty of Science and Agriculture
- Language
- English
- Rights
- University of Fort Hare
- Rights
- All Rights Reserved
- Rights
- Open Access
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UFH Department of Mathematics
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | SOURCE1 | IK Appiah's PhD Thesis Final.pdf | 1 MB | Adobe Acrobat PDF | View Details Download |