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## On D-groupoids, quasigroups and homomorphisms. (English)

In this paper it is proved that there exists a $D$-groupoid $Q(\cdot )$ and systems of identities $\Sigma$ such that $Q(\cdot )$ can not be represented as a homomorphic image of a quasigroup $G(\circ )$ if $Q(\cdot )$ and $G(\circ )$ satisfy the identities of $\Sigma$. Also the smallest sub@-$D$@-groupoid $K$ is constructed such that $Q/K(\ast )$ is a group.