Free subgroups of the fundamental group of the Haiwaiian earring. (English) Zbl 0951.20016
The author gives new and simplified proofs of the theorems of Zastrow and of Cannon-Conner which state that certain naturally-defined subgroups of the fundamental group of the Hawaiian earring and its generalizations are free.
Reviewer: J.W.Cannon (Provo)
MSC:
| 20E06 | Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations |
| 20E07 | Subgroup theorems; subgroup growth |
| 20F34 | Fundamental groups and their automorphisms (group-theoretic aspects) |
| 57M05 | Fundamental group, presentations, free differential calculus |
References:
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| [3] | Eda, K., Free σ-products and noncommutatively slender groups, J. Algebra, 148, 243-263 (1992) · Zbl 0779.20012 |
| [4] | Eda, K., Free σ-products and fundamental groups of subspaces of the plane, Topology Appl., 84, 283-306 (1998) · Zbl 0920.55016 |
| [5] | Higman, G., Unrestricted free products, and variety of topological groups, J. London Math. Soc., 27, 73-81 (1952) · Zbl 0046.02601 |
| [6] | Nöbeling, G., Verallgemeinerung eines satzes von herrn e. specker, Invent. Math., 6, 41-55 (1968) · Zbl 0176.29801 |
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| [8] | A. Zastrow, The non-abelian specker-group is free, preprint.; A. Zastrow, The non-abelian specker-group is free, preprint. · Zbl 0959.20028 |
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