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Two Permutations Product

The product or composite of two permutations

Thus the product of two permutations

Let

Here, the permutation g has been written in such a way that the first row of

For,

Obviously,

Therefore,

**ƒ, g S**_{n}, denoted byThus the product of two permutations

**ƒ**and**g**of degree n denoted by**ƒg**is obtained by first carrying out the operation defined by**ƒ**and then by**g**.Let

**ƒ, g Sn**, andHere, the permutation g has been written in such a way that the first row of

**g**coincides with the second row of**ƒ.**If the product of two permutations**ƒ**and**g**is denoted multiplicatively, i.e. by**ƒg**or**ƒog**then by definitionFor,

**ƒ**replaces**a**_{1}by**b**_{1}and then g replaces**b**_{1}by**c**_{1}so that**ƒg**replaces**a**_{1}by**c**_{1}. Similarly,**ƒg**replaces**a**_{2}by**c**_{2},**a**_{3}by**c**_{3}, …., a_{n}by**c**_{n}.Obviously,

**ƒg**is also a permutation of degree**n**.Thus the product of two permutations of degree**n**is also a permutation of degree**n**.Therefore,

**ƒ g S**_{n}, ∀ ƒ, g S_{n}.**Services: -**Two Permutations Product Homework | Two Permutations Product Homework Help | Two Permutations Product Homework Help Services | Live Two Permutations Product Homework Help | Two Permutations Product Homework Tutors | Online Two Permutations Product Homework Help | Two Permutations Product Tutors | Online Two Permutations Product Tutors | Two Permutations Product Homework Services | Two Permutations ProductSubmit Your Query ???

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