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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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), 309-329 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.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 186 (1973), 309-329
  • MSC: Primary 20F20
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0340433-3
  • MathSciNet review: 0340433