Benign subgroup
= Benign subgroup
{title2=$H=G\cap L$}
A subgroup $H$ of a <finitely generated group> $G$ is benign if some <finitely presented group> $P$ contains $G$ and some <finitely generated subgroup> $L\le P$ satisfies $H=G\cap L$. The subgroup $H$ itself need not be finitely generated. A centralizing <HNN extension> of $P$ along $L$ is finitely presented even when the corresponding intersection subgroup $H$ is infinitely generated.