most recent 30 from http://mathoverflow.net 2013-06-18T06:52:42Z http://mathoverflow.net/feeds/question/18974 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/18974/is-a-normal-subgroup-of-a-finitely-presented-group-finitely-generated-or-normal-f yeshengkui 2010-03-22T04:22:03Z 2010-03-22T04:35:11Z

<p>Let $G$ be a finitely presented group and $N$ a normal subgroup. Is $N$ finitely generated or normally finitely generated? Here normally finitely generation means that for some finite set $S$ of elements in $N$, every element of $N$ can be writen as a product of $G$-conjugation of elements in $S$. Thanks. </p>

http://mathoverflow.net/questions/18974/is-a-normal-subgroup-of-a-finitely-presented-group-finitely-generated-or-normal-f/18975#18975 Steve D 2010-03-22T04:35:11Z 2010-03-22T04:35:11Z

<p>If $G$ is the free group on two generators, then $N$ the commutator subgroup is not finitely generated. If $H$ is any finitely generated, but not finitely presented group, then $H$ is the quotient of a finitely generated free group $G$, with kernel $N$ which is not normally finitely generated.</p> <p>Steve</p>