A Kurosh subgroup theorem for free pro$\mathcal {C}$products of pro$\mathcal {C}$groups
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 by Dion Gildenhuys and Luis Ribes PDF
 Trans. Amer. Math. Soc. 186 (1973), 309329 Request permission
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

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Additional Information
 © Copyright 1973 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 186 (1973), 309329
 MSC: Primary 20F20
 DOI: https://doi.org/10.1090/S00029947197303404333
 MathSciNet review: 0340433