Abstract
Let \(\mathcal{N}\) be a nonempty collection of normal subgroups of finite index of a group G and assume that \(\mathcal{N}\) is filtered from below, i.e., \(\mathcal{N}\) satisfies the following condition:
Then one can make G into a topological group by considering \(\mathcal{N}\) as a fundamental system of neighborhoods of the identity element 1 of G. We refer to the corresponding topology on G as a profinite topology. If every quotient G/N \((N\in \mathcal{N})\) belongs to a certain class \(\mathcal{C}\), we say more specifically that the topology above is a pro - \(\mathcal{C}\) topology.
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© 2010 Springer-Verlag Berlin Heidelberg
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Ribes, L., Zalesskii, P. (2010). Free 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_3
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DOI: https://doi.org/10.1007/978-3-642-01642-4_3
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