most recent 30 from http://mathoverflow.net 2013-05-20T06:39:07Z http://mathoverflow.net/feeds/question/30493 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/30493/elementary-abelian-normal-subgroups-of-a-pro-p-group Colin Reid 2010-07-04T09:07:03Z 2010-07-27T15:53:17Z

<p>Let $P$ be a (finitely generated) pro-$p$ group, and let $E$ be an infinite elementary abelian normal subgroup. Does $E$ necessarily contain a non-trivial finite normal subgroup of $P$? We can think of $E$ as consisting of sequences of elements of $C_p$, with open subgroups $O_X$, where $X$ is a finite subset of the indexing set and $O_X$ consists of the sequences that are zero on $X$. However, I can't think of a way of making $P$ act on these sequences that doesn't leave some finite subgroup invariant. Acting on the indexing set is no good because the orbits would have to be finite, and you'd have a finite normal subgroup consisting of sequences that are zero outside some given orbit.</p>

http://mathoverflow.net/questions/30493/elementary-abelian-normal-subgroups-of-a-pro-p-group/33536#33536 Colin Reid 2010-07-27T15:53:17Z 2010-07-27T15:53:17Z

<p>After talking to Charles Leedham-Green, I now have an example that answers the question (I think). See <a href="http://mathoverflow.net:80/questions/33533/name-this-pro-p-group" rel="nofollow">http://mathoverflow.net:80/questions/33533/name-this-pro-p-group</a>. More interesting examples would still be nice though, particularly if they do not have $C_p \wr C_p$ as an image.</p>