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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| [2] | Eda, K., Free σ-products and non-commutatively slender groups, Journal of Algebra, 148, 243-263 (1992) · Zbl 0779.20012 · doi:10.1016/0021-8693(92)90246-I |
| [3] | K. Eda, Question and homomorphisms on archipelago groups, http://www.logic.info.waseda.ac.jp/∼eda/pdf/question.pdf. |
| [4] | Griffiths, H. B., Infinite products of semi-groups and local connectivity, Proceedings of the London Mathematical Society, 6, 455-480 (1956) · Zbl 0071.01902 · doi:10.1112/plms/s3-6.3.455 |
| [5] | Herfort, W.; Hojka, W., Cotorsion and wild homology, Israel Journal of Mathematics, 221, 275-290 (2017) · Zbl 1421.55012 · doi:10.1007/s11856-017-1566-z |
| [6] | Magnus, W.; Karrass, A.; Solitar, D., Combinatorial Group Theory (2004), Mineola, NY: Dover, Mineola, NY · Zbl 1130.20307 |
| [7] | Morgan, J. W.; Morrison, I., A van Kampen theorem for weak joins, Proceedings of the London Mathematical Society, 53, 562-576 (1986) · Zbl 0609.57002 · doi:10.1112/plms/s3-53.3.562 |
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