# Permute command on symmetric vs alternating groups

Posted 4 months ago
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 Why does this happen? Permute[{0,0,0}, SymmetricGroup[3]] {{0,0,0}} Permute[{0,0,0}, AlternatingGroup[3]] {{0,0,0}, {0,0,0}, {0,0,0}} 
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Posted 4 months ago
 If you interchange two zeros nothing will happen :) In[3]:= Permute[{1, 2, 3}, SymmetricGroup[3]] Out[3]= {{1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}} In[4]:= Permute[{1, 2, 3}, AlternatingGroup[3]] Out[4]= {{1, 2, 3}, {2, 3, 1}, {3, 1, 2}} 
Posted 4 months ago
 But why repeated element for An group but not Sn group?
Posted 4 months ago
 ??????Where do you see a repeated element (or: what do you mean by "repeated element"?)
Posted 4 months ago
 Why does the alternating set have 3 elements all {0,0,0} but symmetric has only one element {0,0,0} instead of 6 copies (number of elements in S3)?
 And in my System (Mma 7.0) I get In[37]:= Permute[{0, 0, 0}, SymmetricGroup[3]] Out[37]= {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}, {0, 0, 0}, {0, 0, 0}, {0, 0, 0}}