2 problems

For $k\geq 2$, let $\sum_{<k}$ be the collection of words in $*_1,\ldots,*_d$ in which each letter occurs at most $k-1$ times. For elements $a,x_1,\ldots,x_d$ of an $s$-step nilpot…

Quotient conjecture for coset nilprogressions. Every coset nilprogression is controlled by a set $A$ containing a finite subgroup which is normal in $A$, such that after quotientin…