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Permutation set acting on another set

asked 2016-05-17 15:40:13 -0500

huhahu gravatar image

How do I make a set of permutation acting on another set?

A4 = AlternatingGroup(4)
r1 = A4("(1,2) (3,4)")
r2 = A4("(1,3) (2,4)")
r3 = A4("(1,4) (2,3)")
N = A4.subgroup([r1, r2, r3]) # generate normal subgroup
LC = A4.cosets(N, side="left")
print LC
print LC[0]*LC[1]

Here I want coset LC[0] act on LC[1]. How do I make it?

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answered 2016-05-19 11:04:35 -0500

TumericTJ gravatar image

Maybe something like this...

A4 = AlternatingGroup(4)
r1 = A4("(1,2) (3,4)")
r2 = A4("(1,3) (2,4)")
r3 = A4("(1,4) (2,3)")
N = A4.subgroup([r1, r2, r3]) # generate normal subgroup
LC = A4.cosets(N, side="left")

elements = []
for i in range(len(LC[0])):
    for j in range(len(LC[1])):
        elements.append( Permutation(LC[0][i]).left_action_product(Permutation(LC[1][j])) )
myset = Set(elements)
myset

Output: {[3, 1, 2, 4], [1, 3, 4, 2], [2, 4, 3, 1], [4, 2, 1, 3]}

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Asked: 2016-05-17 15:38:47 -0500

Seen: 58 times

Last updated: May 19 '16