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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}}
6 Replies

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}}

But why repeated element for An group but not Sn group?

??????

Where do you see a repeated element (or: what do you mean by "repeated element"?)

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)?

Ah, that is the point. I don't know. Try {1,1,1}. And write a letter to Wolfram-Support.

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}}
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