Abstract
For the Jennings group J(k) of substitutions of formal power series with coefficients in a field k of positive characteristic (the Nottingham group), the depth of the powers of its elements is studied. In particular, it is shown that the case of a field with characteristic 2 is completely different from the case of a field with odd prime characteristic. It is also shown that the case of the field k=Z2 differs from the case of other fields with characteristic 2. Explicit embeddings of the groups Zpm and Zp⊕Zp in J(Zp) are constructed.
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