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The production of Σ0 baryons in the nuclear reaction p (3.5 GeV) + Nb (corresponding to sNN=3.18 GeV) is studied with the detector set-up HADES at GSI, Darmstadt. Σ0s were identified via the decay Σ0→Λγ with subsequent decays Λ→pπ− in coincidence with a e+e− pair from either external (γ→e+e−) or internal (Dalitz decay γ⁎→e+e−) gamma conversions. The differential Σ0 cross section integrated over the detector acceptance, i.e. the rapidity interval 0.5<y<1.1, has been extracted as ΔσΣ0=2.3±(0.2)stat±(−0.6+0.6)sys±(0.2)norm mb, yielding the inclusive production cross section in full phase space σΣ0total=5.8±(0.5)stat±(−1.4+1.4)sys±(0.6)norm±(1.7)extrapol mb by averaging over different extrapolation methods. The Λall/Σ0 ratio within the HADES acceptance is equal to 2.3±(0.2)stat±(−0.6+0.6)sys. The obtained rapidity and momentum distributions are compared to transport model calculations. The Σ0 yield agrees with the statistical model of particle production in nuclear reactions. Keywords: Hyperons, Strangeness, Proton, Nucleus.