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We consider three-loop radiative-recoil corrections to hyperfine splitting inmuonium generated by diagrams with one-loop radiative photon insertions both inthe electron and muon lines. An analytic result for these nonlogarithmiccorrections of order $\alpha(Z^2\alpha)(Z\alpha)(m/M)\widetilde E_F$ isobtained. This result constitutes a next step in the implementation of theprogram of reduction of the theoretical uncertainty of hyperfine splittingbelow 10 Hz.Comment: 11 pages, 3 figures, 1 tabl

Three-loop radiative-recoil corrections to hyperfine splitting generated by one-loop fermion factors