ORDER CLASSES OF SYMMETRIC GROUPS
Bilal N. Al-Hasanat1, Azhana Ahmad2, Hajar Sulaiman3, Faisal Ababneh4
1,2,3School of Mathematical Sciences
Universiti Sains Malaysia
11800 USM, Pulau Pinang, MALAYSIA
4 Department of Mathematics
Al-Hussein Bin Talal University
Ma'an, JORDAN
Abstract. The order of an element x in a finite group G is the smallest positive integer k, such that xk is the group identity. The set of all possible such orders joint with the number of elements that each order referred to, is called the order classes of G. In this paper, the order classes of symmetric groups is derived.
AMS Subject classification: 20B30, 20B05
Keywords and phrases: element order, order classes, simple and non-simple permutations


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DOI: 10.12732/ijam.v26i4.8

Volume: 26
Issue: 4
Year: 2013