How to make group act on a set?

Group

asked 2016-09-10 13:26:03 +0200

sageuser
3 ●1 ●3

updated 2016-09-11 13:50:27 +0200

How to make group act on set? For example, the set is s A={1, 2} and the group is SymmetricGroup(3). I would like to calculate the output put each permutation map of elements of Symmetric Group so that I can calculate normaizer and stablizer.

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answered 2016-09-12 04:07:51 +0200

calc314
4191 ●22 ●48 ●113

To compute the group action you want:

G=SymmetricGroup(3)
A={1,2}
for g in G:
    for a in A:
        print str(g)+' acts on '+str(a)+' to give '+str(g(a))

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Comments

I am not sure that this computes what the OP wants: you get for instance

(1,3,2) acts on 1 to give 3

while $3$ is not in A.

B r u n o ( 2016-09-12 19:37:17 +0200 )edit

Yes, this is what I exactly want!! I didn't know the group elements could be used as function.

sageuser ( 2016-09-14 03:20:45 +0200 )edit

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Asked: 2016-09-10 13:26:03 +0200

Seen: 319 times

Last updated: Sep 12 '16

How to make group act on a set? edit