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I used notation of paper of Jorge Almeida "Dynamics of implicit operations and tameness of pseudovarities of group" in my question.

Let $V$ be a pseudovarity of finite groups. We know that every element $\pi$ of a $A$-generated free pro-$V$ group can be viewed as a implicit operation.

I want an example of non-computable implicit operation.

Mike Pierce
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user182085
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    Could you define your terms to make this question more accessible? – Noah Schweber Jun 18 '15 at 15:22
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    A trivial example in two generators is $\prod x^{n!}y^{a_nn!}$ where $a_n\ge 1$ is any increasing non-computable sequence of positive integers. – YCor Jun 18 '15 at 17:40
  • @Ycor could you please tell me why this implicit operation is not computable? I have another example and I proved that that one is not computable. But I can not prove this one is not computable – user182085 Jun 30 '15 at 13:30

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