Profinite Groups pp 119-158 | Cite as
Some Special Profinite Groups
Chapter
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Abstract
Let G be a profinite group and x∈G. Since \(\widehat {\mathbf{Z}}\) is a free profinite group on {1}, there is a unique epimorphism
such that φ(1)=x. Given \(\lambda \in \widehat {\mathbf{Z}}\), define x λ =φ(λ).
$$\varphi :\widehat{\mathbf{Z}}\longrightarrow \overline {\langle x\rangle }$$
Keywords
Abelian Group Normal Subgroup Open Subgroup Congruence Subgroup Frobenius Group
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer-Verlag Berlin Heidelberg 2010