An example of a soluble group
- From: Loius Burnside <burnside.louis@xxxxxxxxx>
- Date: Sat, 06 Oct 2007 18:31:30 -0700
Hi everyone!
I was wondering about
"a finitely generated soluble group G such that its commutator
subgroup is not finitely generated".
1. It's well known that a f.g. nilpotent group (actually a
polycyclic)
has the MAX condition (which is equivalent to all its subgroup being
f.g.).
In particular, G cannot be cyclic, abelian, nilpotent, supersolvable,
polycyclic.
2. Clearly, G cannot be finite.
3. Also, G cannot be simple (in this case G would be abelian).
4. I found some examples of non-f.g. soluble groups: UT(3,Q), Dih(Q),
Z(p^infty) wr Z(p^infty).
Can anyone help me with that?
Best regards,
Louis.
.
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