A Kurosh subgroup theorem for free pro-𝒞-products of pro-𝒞-groups

Gildenhuys, Dion; Ribes, Luis

doi:10.1090/S0002-9947-1973-0340433-3

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

Trans. Amer. Math. Soc. 186 (1973), 309-329

DOI: https://doi.org/10.1090/S0002-9947-1973-0340433-3

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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.

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