TITLE

On the Conjugacy Classes, Centers and Representation of the Groups Sn and Dn

AUTHOR(S)
Samaila, D.; Abba, B. Ibrahim; Pur, M. Pius
PUB. DATE
March 2013
SOURCE
International Journal of Pure & Applied Sciences & Technology;Mar2013, Vol. 15 Issue 1, p87
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The desire in this paper is to critically examine the properties of the elements of the symmetric group Sn and the dihedral group Dn. It has always been a difficult task in determining the behaviors of reflections and rotational symmetries in these symmetry groups and how much information can be obtained from there symmetries. We therefore study the nature and properties of these symmetry elements including the conjugacy class size in both Sn and Dn. It was found that the conjugacy classes of Sn are determined by their cycle type while that of Dn is a special case, where the relation "Conjugacy" is an equivalence relation. The representations of the conjugacy class size of Dn reveals that the order of the centers of Dn are 1 (for nodd) and 2 (for n-even), and consequently, leading to two different class equations of Dn.
ACCESSION #
87991943

 

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