Archipelago groups are locally free. Corrigendum to: “Cotorsion and wild homology”. (English) Zbl 1491.55013
Summary: An Archipelago group is the quotient of the topologist’s product \(G = \circledast_{i \ge 1}G_i\) of a sequence \((G_i)_{i \ge 1}\) of groups modulo the normal closure of the subset \(\bigcup_{i \ge 1}G_i\) in \(G\). In this note we provide a simple proof of a result from [the authors, ibid. 221, No. 1, 275–290 (2017; Zbl 1421.55012)], namely that Archipelago groups are locally free.
MSC:
55Q20 | Homotopy groups of wedges, joins, and simple spaces |
20J06 | Cohomology of groups |
57M30 | Wild embeddings |
20K20 | Torsion-free groups, infinite rank |
20E06 | Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations |
20F38 | Other groups related to topology or analysis |
Citations:
Zbl 1421.55012References:
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[6] | Magnus, W.; Karrass, A.; Solitar, D., Combinatorial Group Theory (2004), Mineola, NY: Dover, Mineola, NY · Zbl 1130.20307 |
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