This paper investigates the full compressible magnetohydrodynamic system in three-dimensional exterior domains. For the initial-boundary-value problem of this system with slip boundary condition for the velocity, adiabatic one for the temperature, and perfect one for the magnetic field, we establish the global existence and uniqueness of strong solutions, under the condition that the initial data are of small energy but possibly large oscillations, where the initial density and temperature are both allowed to vanish. Moreover, the large-time behavior of the strong solutions is also shown.

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