Exponent of Self-similar finite $p$-groups

Alex Carrazedo Dantas, Emerson de Melo

Let $p$ be a prime and $G$ a pro-$p$ group of finite rank that admits a faithful, self-similar action on the $p$-ary rooted tree. We prove that if the set $\{g\in G \ | \ g^{p^n}=1…