Abstract
In § l of this article, we study group-theoretical properties of some automorphism group Ψ* of the meta-abelian quotient § of a free pro-l group § of rank two, and show that the conjugacy class of some element of order two of Ψ* is not determined by the action induced on the abelian quotient § of § in the case of § = 2. In § 2 we apply the results to the outer Galois representation § attached to the curve C deleted one point from an elliptic curve E, and give an example that §c does not factor through the l-adic representation attached to E.
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