Abstract
We study the augmentation quotients of the IA-automorphism group of a free group and a free metabelian group. First, for any group G , we construct a lift of the k ‐th Johnson homomorphism of the automorphism group of G to the k ‐th augmentation quotient of the IA-automorphism group of G . Then we study the images of these homomorphisms for the case where G is a free group and a free metabelian group. As a corollary, we detect a Z‐free part in each of the augmentation quotients, which can not be detected by the abelianization of the IA-automorphism group. 20F28; 16S34
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