Mann’s Lemma and \(Z\)-Cyclic Whist Tournaments

The main result of this study is that if \(p,q\) are primes such that \(q \equiv 3 (mod 4),q \leq 7,p \equiv 1 (mod 4), hef(q-1,p^{n-1} (p – 1)) =2\) and if there exists a Z-cyclic Wh(q+ 1) then a Z-cyclic Wh\(( qp^n + 1)\) exists forall \(n \geq 0\). As an ingredient sufficient for this result we prove a version of Mann’s Lemma in the ring \(Z_{qp^n}\).