Analysis of 9700 events, containing at least one observed neutral or charged decay, produced by 6-BeVc protons in the LRL 72-in. liquid-hydrogen bubble chamber has yielded 1746 examples of the reaction proton+proton-->hyperon+K meson+nucleon. Production cross sections for these three-body reactions are as follows: σ(ΛK+p)=54-5+3μb, σ(Σ0K+p)=17-2+4μb, σ(Σ+K0p)=26+/-4μb, σ(Σ+K+n)=57+/-7μb. Strong N* production is observed in all channels. In particular, one or more T=12 resonant states with mass near 1700 MeVc2, decaying into ΛK+, and a T=32 resonance with mass 1920 MeVc2, decaying into Σ+K+, are produced. In all cases the data are consistent with a production process dominated by a single-pion-exchange mechanism. No evidence is found for a dibaryon state in either the Λ-proton or Σ-nucleon system.