- Title
- The classification of fuzzy groups of finite cyclic groups Zpn Zqm Zr and Zp1 Zp2 Zpn for distinct prime numbers p; q; r; p1; p2; ; pn and n;m 2 Z+
- Creator
- Munywoki, Michael Mbindyo
- Subject
- Fuzzy sets Finite groups
- Date
- 2018
- Type
- Thesis
- Type
- Doctoral
- Type
- DPhil
- Identifier
- http://hdl.handle.net/10353/17817
- Identifier
- vital:41295
- Description
- Let G be the cyclic group Zpn _ Zqm _ Zr where p; q; r are distinct primes and n;m 2 Z+. Using the criss-cut method by Murali and Makamba, we determine in general the number of distinct fuzzy subgroups of G. This is achieved by using the maximal chains of subgroups of the respective groups, and the equivalence relation given in their research papers. For cases of m, the number of fuzzy subgroups is _rst given, from which the general pattern for G is achieved. Murali and Makamba discussed the number of fuzzy subgroups of Zpn _ Zqm using the cross-cut method. A brief revisit of the group Zpn _Zqm is done using the criss-cut method. The formulae for _nding the number of distinct fuzzy subgroups in each of the cases is given and proofs provided. Furthermore, we classify the fuzzy subgroups of the group Zp1_Zp2__ _ __Zpn for p1; p2; _ _ _ ; pn distinct primes and n 2 Z+ using the criss-cut method. An algorithm for counting the distinct fuzzy subgroups of this group is developed.
- Format
- 181 leaves
- Format
- Publisher
- University of Fort Hare
- Publisher
- Faculty of Science and Agriculture
- Language
- English
- Rights
- University of Fort Hare
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UFH Department of Mathematics
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details | SOURCE1 | PhD (Mathematics) MUNYWOKI - May 2018.pdf | 808 KB | Adobe Acrobat PDF | View Details |