Abstract: It is proved that there exist no Menon difference sets in groups of order 4p²(p=5, p=3(mod 4)) with homomorphic images Z₄×Z_p and point out that the Turyn's exponent bound can be improved in certain case.

Key words: Menon difference sets, intersection numbers, character table, complete cyclic basis

摘要： 证明了具有同态象Z₄×Z_p的4p²阶群中不存在Menon差集(p≥5, p≡3(mod 4)), 并指出在某些情形下Turyn的指数界可以改善。

关键词: Menon差集, 相交数, 特征标表, 完全循环基