Wikipedia Talk:Lamplighter group

Questions about the Lamplighter group

I got here by accident, and I'm not really an expert in
the lamplighter group, and the wreath product definition
didn't really help.  So I got the presentation from
http://arxiv.org/abs/math.GR/0312331 and worked the
rest out on my own (getting it wrong on the first try).

But the definition there defines a finitely generated group, and the
wreath product definition apparently defines an uncountable group,
which cannot even be countably generated.  If we are talking about
Growth rate (group theory) (which seems to be the motivating feature
for this article), that is defined with respect to a particular
generating set, and it looks like that set needs to be finite.
Perhaps we need to refer to the finitely supported subgroup of

  \bigoplus_{(-\infty, +\infty)} \mathbb{Z}/2\mathbb{Z},

but I don't know the name for that.

  \bigcup_{n=0}^\infty \bigoplus_{(-n, +n)}
  \mathbb{Z}/2\mathbb{Z}

is only approximately correct.

A second question is a proof that the group is a solvable group.
Anyone?  Dan Hoey 03:07, 9 March 2007 (UTC) mod Dan Hoey 14:08, 9
March 2007 (UTC)