Abstract
Let \(\mathcal{C}\) be a nonempty class of finite groups [this will always mean that \(\mathcal{C}\) contains all the isomorphic images of the groups in \(\mathcal{C}\)]. Define a pro - \(\mathcal{C}\) group G as an inverse limit
of a surjective inverse system {G i ,φ ij ,I} of groups G i in \(\mathcal{C}\), where each group G i is assumed to have the discrete topology. We think of such a pro - \(\mathcal{C}\) group G as a topological group, whose topology is inherited from the product topology on ∏ i∈I G i .
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© 2010 Springer-Verlag Berlin Heidelberg
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Ribes, L., Zalesskii, P. (2010). Profinite Groups. In: Profinite Groups. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01642-4_2
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DOI: https://doi.org/10.1007/978-3-642-01642-4_2
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01641-7
Online ISBN: 978-3-642-01642-4
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