Unbounded symmetrysets

Unbounded symmetrysets R Z_pⁿ are introduced which, in the presence of a Jacobi condition, are classified and can be written as R = Z_p^n₁ + + Z_pⁿ_k (inner direct sum), where n_i n for all i = 1, , k. The properties of these unbounded symmetrysets are easily verified for the set R of roots of Witt Lie algebras. This paper is a step in the direction of classifying simple Lie algebras of characteristic, p, by studying their rootsystems.