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Using techniques from TRO equivalence of masa bimodules we prove varioustransference results: We show that when $\alpha$ is a group homomorphism whichpushes forward the Haar measure of $G$ to a measure absolutely continuous withrespect to the Haar measure on $H$, then $(\alpha\times\alpha)^{-1}$ preservessets of compact operator synthesis, and conversely when $\alpha$ is onto. Wealso prove similar preservation results for operator Ditkin sets and operatorM-sets, obtaining preservation results for M-sets as corollaries. Some of theseresults extend or complement existing results of Ludwig, Shulman, Todorov andTurowska.

Synthetic properties of locally compact groups: preservation and transference