Abstract
Throughout this chapter \(\mathcal{C}\) denotes usually an NE-formation of finite groups, i.e., \(\mathcal{C}\) is a nonempty class of finite groups closed under taking normal subgroups, homomorphic images and extensions. Equivalently, \(\mathcal{C}\) is the class of all finite Δ-groups, where Δ is a set of finite simple groups (see Section 2.1). In particular, \(\mathcal{C}\) could be the class of all finite groups, the class of all finite solvable groups, etc. Often we require in addition that \(\mathcal{C}\) ‘involves two different primes’, that is, that there exists a group in \(\mathcal{C}\) whose order is divisible by at least two different prime numbers. In this chapter \(\varSigma_{\mathcal{C}}\) denotes the collection of all finite simple groups in \(\mathcal{C}\), and Σ denotes the class of all finite simple groups.
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© 2010 Springer-Verlag Berlin Heidelberg
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Ribes, L., Zalesskii, P. (2010). Normal Subgroups of Free Pro - \({\cal C}\) 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_8
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DOI: https://doi.org/10.1007/978-3-642-01642-4_8
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