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On automorphisms of commutative Moufang loops

Abstract It is proved that the automorphism group of any commutative Moufang loop Q is an extension of the group F(1) consisting of all automorphisms of the loop Q which induce the identity mapping onto the factor-loop Q/A(Q) of Q by means of the automorphism group of the abelian group Q/A(Q). We investigate the structure of the group F(1) in the cases where the loop Q is either centrally nilpotent, or finitely generated, or is a ZA-loop.