# 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

add a comment

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.

Asked: **
2013-01-27 00:29:16 -0500
**

Seen: **182 times**

Last updated: **Jan 27 '13**

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.