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For n ≥ 1, let Sn denote the group of all permutations on n symbols. Which of the following statement is true?

  1. S3 has an element of order 4
  2. S4 has an element of order 6
  3. S4 has an element of order 5
  4. S5 has an element of order 6.

Answer (Detailed Solution Below)

Option 4 : S5 has an element of order 6.

Detailed Solution

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Solution - Sn denote the group of all permutations on n symbols.  

In \(S_3\) possible Order be lcm (3,1) so maximum possibility be 3 

Therefore, Option 1) is wrong 

In, \(S_4 \)  maximum possibility be 4 

Therefore, Option 2) and Option 3) is also wrong 

In, \(S_5\) has maximum possibility be lcm (3,2) =6 

Therefore, Correct Option is Option 4).

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