Ternary universal integral quadratic forms over real quadratic fields

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Abstract. Menon difference sets have the parameters (4N 2, 2N 2 + N, N 2 5: N). In this paper, a necessary condition for Menon difference sets in groups of the form Z~p x Z2p • Gq, where Gq is an abelian q-group and p, q are distinct prime numbers, will be proved. We will also focus on the groups Z2p q X ~2pq and give constraints on the magnitudes ofp and q. Finally, we show that if the group Z6v • Z6p contains a Menon difference set, then p = 3 or 13 only.