$p$-nilpotency criteria for some verbal subgroups

Yerko Contreras Rojas, Valentina Grazian, Carmine Monetta

Let $G$ be a finite group, let $p$ be a prime and let $w$ be a group-word. We say that $G$ satisfies $P(w,p)$ if the prime $p$ divides the order of $xy$ for every $w$-value $x$ in…