  Let $p$ be a rational prime, let $F$ denote a finite, unramified extension of
$\mathbb{Q}_p$, let $K$ be the completion of the maximal unramified extension
of $\mathbb{Q}_p$, and let $\overline{K}$ be some fixed algebraic closure of
$K$. Let $A$ be an abelian variety defined over $F$, with good reduction, let
$\mathcal{A}$ denote the N\'eron model of $A$ over ${\rm Spec}(\mathcal{O}_F)$,
and let $\widehat{\mathcal{A}}$ be the formal completion of $\mathcal{A}$ along
the identity of its special fiber, i.e. the formal group of $A$.
  In this work, we prove two results concerning the ramification of $p$-power
torsion points on $\widehat{\mathcal{A}}$. One of our main results describes
conditions on $\widehat{\mathcal{A}}$, base changed to
$\text{Spf}(\mathcal{O}_K) $, for which the field
$K(\widehat{\mathcal{A}}[p])/K$ is a tamely ramified extension where
$\widehat{\mathcal{A}}[p]$ denotes the group of $p$-torsion points of
$\widehat{\mathcal{A}}$ over $\mathcal{O}_{\overline{K}}$. This result
generalizes previous work when $A$ is $1$-dimensional and work of
Arias-de-Reyna when $A$ is the Jacobian of certain genus 2 hyperelliptic
curves.
