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The Free Alternative Nil-Superalgebra of Index n on One Odd Generator

A base of the free alternative nil-superalgebra of index n, for n ≥ 3, on one odd generator is constructed. In particular, its index of solvability is computed. As a corollary over a field of characteristic zero an infinite family of solvable alternative algebras which are not associative of arbitrary big solvability index with explicit multiplication table is obtained.