Algebra-Permutation Groups [IAS (Admin.) Mains Mathematics]: Questions 1 - 2 of 2

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Question 1

Appeared in Year: 2013

Describe in Detail Subjective▾

What is the maximal possible order of an element in ? Give an example of such an element. How many element՚s will there be in of that order? (Paper II)

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Explanation

NOTE:- For convenience, we denote an n-cycle by then all the possible disjoint cycle structures of element of according to longest cycle lengths left to right, we have

… (1267 more equations) …

Question 2

Appeared in Year: 2013

Write in Short Short Answer▾

What are the orders of the following permutations in so?

And (Paper II)

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