Some Result about a Product of Conjugate Cycles | Zendy

Shaimaa S. Al-Bundi | Zendy

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Some Result about a Product of Conjugate Cycles

Author(s) -

Shaimaa S. Al-Bundi

Publication year - 2011

Publication title -

journal of al-nahrain university-science

Language(s) - English

Resource type - Journals

eISSN - 2519-0881

pISSN - 1814-5922

DOI - 10.22401/jnus.14.4.22

Subject(s) - permutation (music) , mathematics , combinatorics , product (mathematics) , generalization , commutator , order (exchange) , conjugate , discrete mathematics , algebra over a field , pure mathematics , physics , mathematical analysis , geometry , lie conformal algebra , finance , acoustics , economics

The aim of this paper is to give a generalization of the theorem that, for n 5, every even permutation defined on n symbols is commutator a b a -1 b -1 of even permutations a and b. In particular, [3n/4] L n is shown to be the necessary and sufficient condition on L, in order that every even permutation defined on n 5 symbols can be expressed as a product of two cycles, each of length L. Results follow, including every odd permutation is a product of a cycle of length L and a cycle of length L + 1.

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