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Summary form only given.In principal, one could use microwave driving of hyperfine or Zeeman sublevels of the nuclear levels. But the large difference in the frequencies of the driven and amplifying transitions leads to a number of difficulties, which could be essentially reduced in case of optical driving. However the absence of optical transitions in the structure of nuclear levels does not allow direct driving of nuclear transitions by laser radiation. We show that coherent optical driving of the electronic transitions can provide amplification without inversion (AWI) at gamma-ray nuclear transition in cases when the structure of the electronic levels is essentially modified by excitation of nucleus.