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Transposition

A cycle of length two is called a transposition. It is a

Here

A transposition is a permutation

Suppose that

Thus

For brevity we write

Rather than the fuller function table we have used heretofore. Note that a transposition

**2-cycle**. For example (**1 2), (2 3), (1 3)**are three transpositions in**S**_{3}.Here

**(2, 3)**is a**2-cycle**such that image of**2**is**3**and the image of**3**is**2**and the remaining missing elements are fixed or invariant.**Alternative definition of transposition**A transposition is a permutation

**ƒ**that moves exactly two elements.Suppose that

**ƒ**moves**a, b**, in which case**(a) ƒ = b**and**(b) ƒ = a**.Thus

**ƒ**has the formFor brevity we write

**ƒ = (a, b) or ƒ = (b, a)**Rather than the fuller function table we have used heretofore. Note that a transposition

**ƒ**is an element of order**2**:**ƒ**^{2}= I ƒ^{-1}= ƒ.**Services: -**Transposition Homework | Transposition Homework Help | Transposition Homework Help Services | Live Transposition Homework Help | Transposition Homework Tutors | Online Transposition Homework Help | Transposition Tutors | Online Transposition Tutors | Transposition Homework Services | TranspositionSubmit Your Query ???

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