Symmetric colorings of finite groups
Date
2015-05-06
Authors
Phakathi, Jabulani
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Abstract
Let G be a finite group and let r ∈ N. A coloring of G is any mapping
: G −→ {1, 2, 3, ..., r}. Colorings of G, and are equivalent if there exists an
element g in G such that (xg−1) = (x) for all x in G. A coloring of a finite group
G is called symmetric with respect to an element g in G if (gx−1g) = (x) for all
x ∈ G. We derive formulae for computing the number of symmetric colorings and the
number of equivalence classes of symmetric colorings for some classes of finite groups
Description
A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. December 2014.