Ramification groups of Galois extensions over local fields of positive characteristic with Galois group isomorphic to the group of unitriangular matrices

We study the ramification groups of finite Galois extensions $L\mathrm{/}K$ of a complete discrete valuation field $K$ of equal characteristic $p>0$ with perfect residue field and Galois group isomorphic to the group of unitriangular matrices $U{T}_n({\mathbb{F}}_p)$ over ${\mathbb{F}}_p$. We show that the upper ramification breaks can be expressed as a linear function of the valuation of the entries of a matrix directly constructed from the coefficients of a defining equation of the extension. This allows us to compute the ramification groups without using any elements of $L-K$.