Classification of p-adic 6-dimensional filiform Leibniz algebras by   solution of x^q=a
  In this paper we study the $p$-adic equation $x^q=a$ over the field of $p$-adic numbers. We construct an algorithm of calculation of criteria of solvability in the case of $q=p^m$ and present a computer program to compute the criteria for fixed value of $m \leq p-1$. Moreover, using this solvability criteria for $q=2,3,4,5,6$, we classify $p$-adic 6-dimensional filiform Leibniz algebras. 
M. Ladra, B.A. Omirov and U.A. Rozikov
math.RA math.NT