Symmetric colorings of finite groups
| dc.contributor.author | Phakathi, Jabulani | |
| dc.date.accessioned | 2019-04-04T08:37:26Z | |
| dc.date.available | 2019-04-04T08:37:26Z | |
| dc.date.issued | 2018 | |
| dc.description | A Thesis presented for the degree of Doctor of Philosophy, 2018 | en_ZA |
| dc.description.abstract | Given a finite group G and r ∈ N, an r-coloring(or coloring) of G is a mapping χ : G −→ {1,2,3,...,r}. The group G naturally acts on its colorings by χ(xg−1) = χ(x). Colorings χ and ψ are equivalent if there is g ∈ G such that χ(xg−1) = ψ(x) for all x ∈ G. A coloring χ of G is called symmetric if there is g ∈ G such that χ(gx−1g) = χ(x) for all x ∈ G. Let |Sr(G)| denote the number of symmetric rcolorings of G and |Sr(G)/ ∼ | the number of equivalence classes of symmetric r-colorings of G. We present methods for computing |Sr(G)/ ∼ | and |Sr(G)| and derive explicit formulas in some cases, in particular cyclic group Zn and the dihedral group Dn. | en_ZA |
| dc.description.librarian | XL2019 | en_ZA |
| dc.format.extent | Online resource (vii, 43 leaves) | |
| dc.identifier.citation | Phakathi, Jabulani (2018) Symmetric colorings of finite groups, University of the Witwatersrand, Johannesburg, <http://hdl.handle.net/10539/26656> | |
| dc.identifier.uri | https://hdl.handle.net/10539/26656 | |
| dc.language.iso | en | en_ZA |
| dc.phd.title | PhD | en_ZA |
| dc.subject.lcsh | Finite simple groups | |
| dc.subject.lcsh | Number theory | |
| dc.title | Symmetric colorings of finite groups | en_ZA |
| dc.type | Thesis | en_ZA |