Measurement of the Branching Fractions of the Cabibbo-favored Decays Λ_c⁺ → Λ<i>k</i>_s⁰ <i>k</i>⁺ and Λ_c⁺ → Ξ⁰<i>k</i>_s⁰ Π⁺ and Search for Λ_c⁺ → Σ⁰<i>k</i>_s⁰ <i>k</i>⁺

Based on e(+)e(-) collision data corresponding to an integrated luminosity of about 4.5 fb(-1) collected at center-of-mass energies between 4599.53 and 4698.82 MeV with the BESIII detector, the absolute branching fraction of the Cabibbo-favored decay Lambda(+)(c) -> Lambda K-S(0) K+ is measured to be (3.12 +/- 0.46 +/- 0.15) x 10(-3). Combined with a previous measurement from the BESIII Collaboration, the branching fraction of the decay Lambda(+)(c) -> Lambda K-S(0) K+ is calculated to be (3.07 +/- 0.26 +/- 0.13) x 10(-3). The decay Lambda(+)(c) -> Xi K-0(S)0 pi(+) is observed for the first time with a statistical significance of 6.6 sigma, and its branching fraction is determined to be (3.70 +/- 0.60 +/- 0.21) x 10(-3). In addition, a search for the decay Lambda(+)(c) -> Sigma K-0(S)0 K+ is performed, and its branching fraction is determined to be (0.80(-0.24)(+0.28) +/- 0.16) x 10(-3), corresponding to an upper limit of 1.28 x 10(-3) at a 90% confidence level. These measurements provide new information that can be used to distinguish between theoretical models.