2 problems

Let $G$ be a finitely generated group of rank $n$. An ordered $n$-tuple is normally generating when its components normally generate $G$, and its recalcitrance is the least number…

Let $G$ be a finitely generated group of rank $n$. An M-transformation replaces one component $s_i$ of an $n$-tuple by $s_iw$, where $w$ lies in the normal closure of the other com…