# permutation representation

Dear all

Does sage support groups such as Frobenius groups or general affine group. How can I find the permutation representation of an arbitrary group.

Best regrad

permutation representation

Dear all

Does sage support groups such as Frobenius groups or general affine group. How can I find the permutation representation of an arbitrary group.

Best regrad

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0

There isn't a general construction of Frobenius groups in Sage currently, although there are many specific ones that can be constructed as members of other collections of groups, e.g. the symmetric group on 3 letters is a Frobenius group:

```
sage: G = SymmetricGroup(3)
```

Is it a Frobenius group? Let's check:

```
for g in G:
if not g.is_one():
fixed = [ x for x in [1..3] if g(x) == x ]
print "elt: ", g, "fixed set: ", fixed
```

returns:

```
elt: (2,3) fixed set: [1]
elt: (1,2) fixed set: [3]
elt: (1,2,3) fixed set: []
elt: (1,3,2) fixed set: []
elt: (1,3) fixed set: [2]
```

Yep.

I don't quite understand your second question. Any finite group can be embedded in a permutation group by its left or right action on itself. This is a basic theorem.

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Asked: ** 2013-01-27 07:29:16 +0200 **

Seen: **281 times**

Last updated: **Jan 28 '13**

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