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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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.

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Keywords: Profinite group, pro-<!– MATH $\mathcal {C}$ –> <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\mathcal {C}$">-group, free product, coproduct, projective limit, pointed topological space, compact, totally disconnected
Article copyright: © Copyright 1973 American Mathematical Society