Abstract
Menon difference sets have the parameters (4N2, 2N2±N,N2±N). In this paper, a necessary condition for Menon difference sets in groups of the formZ2p×Z2p×Gq, whereGq is an abelianq-group andp, q are distinct prime numbers, will be proved. We will also focus on the groupsZ2pq×Z2pq and give constraints on the magnitudes ofp andq. Finally, we show that if the groupZ6p×Z6p contains a Menon difference set, thenp=3 or 13 only.
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