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[answered] Let A(n) be the set of all permutations of {1, 2, 3, . , n}


?Let A(n) be the set of all permutations of {1, 2, 3, . . . , n} with sign 1. Find examples of subgroups of A(4) having orders 1, 2, 3, 4, and 12.


The alternating group on 1, 2,3, 4 is 1 , 12 34 , 13 24 , 14 23 , 13 12 , 12 13 , 14 12 , A4 .

 

12

 

14

 

,

 

14

 

13

 

,

 

13

 

14

 

,

 

24

 

23

 

,

 

23

 

24 Here 1 is the identity permutation.

 

Subgroups of A4 order 1 are...

 


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