  A latin bitrade is a pair of partial latin squares which are disjoint, occupy
the same set of non-empty cells, and whose corresponding rows and columns
contain the same set of entries. Dr\'apal (\cite{Dr9}) showed that a latin
bitrade is equivalent to three derangements whose product is the identity and
whose cycles pairwise have at most one point in common. By letting a group act
on itself by right translation, we show how some latin bitrades may be derived
from groups without specifying an independent group action. Properties of latin
trades such as homogeneousness, minimality (via thinness) and orthogonality may
also be encoded succinctly within the group structure. We apply the
construction to some well-known groups, constructing previously unknown latin
bitrades. In particular, we show the existence of minimal, $k$-homogeneous
latin trades for each odd $k\geq 3$. In some cases these are the smallest known
such examples.
