Transitive resolvable idempotent quasigroups and large sets of resolvable Mendelsohn triple systems

We first define a transitive resolvable idempotent quasigroup (TRIQ), and show that a TRIQ of order vv exists if and only if 3∣v3∣v and v⁄≡2(mod4). Then we use TRIQ to present a tripling construction for large sets of resolvable Mendelsohn triple systems LRMTS(v)s, which improves an earlier version of tripling construction by Kang. As an application we obtain an LRMTS(4⋅3n) for any integer n≥1n≥1, which provides an infinite family of even orders.