3 problems

Let $F_{g,c}$ be the free-nilpotent Lie algebra with $g\ge 2$ generators and nilpotency class $c\ge 3$. A CPA-structure is central when its products take values in the center of…

Let $F_{2,c}$ be the free-nilpotent Lie algebra on two generators of class $c\ge 3$. A two-generated nilpotent Lie algebra has property $F$ if, for every generating pair $(x,y)$, e…

Let $F_{g,c}$ be the free-nilpotent Lie algebra with $g$ generators and nilpotency class $c$, where $g\ge 2$ and $c\ge 2$. A central CPA-structure is a CPA-structure whose products…