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For a rosy theory, we give a canonical surjective homomorphism from a Lascargroup over $A=\acl^{eq}(A)$ to a first homology group of a strong type over$A$, and we describe its kernel by an invariant equivalence relation. As aconsequence, we show that the first homology groups of strong types in rosytheories have the cardinalities of one or at least $2^{\aleph_0}$. We give twoexamples of rosy theories having non trivial first homology groups of strongtypes over $\acl^{eq}(\emptyset)$. In these examples, these two homology groupsare exactly isomorphic to their Lascar group over $\acl^{eq}(\emptyset)$.

Lascar groups and the first homology groups of strong types in rosy theories