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Transactions of the American Mathematical Society

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A Kurosh subgroup theorem for free pro- $ \mathcal{C}$-products of pro- $ \mathcal{C}$-groups


Authors: Dion Gildenhuys and Luis Ribes
Journal: Trans. Amer. Math. Soc. 186 (1973), 309-329
MSC: Primary 20F20
MathSciNet review: 0340433
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Abstract: Let $ \mathcal{C}$ be a class of finite groups, closed under finite products, subgroups and homomorphic images. In this paper we define and study free pro- $ \mathcal{C}$-products of pro- $ \mathcal{C}$-groups indexed by a pointed topological space. Our main result is a structure theorem for open subgroups of such free products along the lines of the Kurosh subgroup theorem for abstract groups. As a consequence we obtain that open subgroups of free pro- $ \mathcal{C}$-groups on a pointed topological space, are free pro- $ \mathcal{C}$-groups on (compact, totally disconnected) pointed topological spaces.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0340433-3
Keywords: Profinite group, pro- $ \mathcal{C}$-group, free product, coproduct, projective limit, pointed topological space, compact, totally disconnected
Article copyright: © Copyright 1973 American Mathematical Society