In this work we introduce the notion of weak quasi groups, that are,
quasi-group operations defined almost everywhere on some set. Then we present
sufficient conditions for an expansive ergodic map $T:X\to X$ to be an
automorphism for some topological weak quasi group. Therefore, we find out an
Abelian topological weak group operation and a standard decomposition of the
dynamics of $T$ in terms of $T$-invariant weak sub-groups.