Three articles on one-relator groups by Wilhelm Magnus
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912210758926336 |
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| author | Nyberg-Brodda, Carl-Fredrik |
| author_facet | Nyberg-Brodda, Carl-Fredrik |
| contents | This is an English translation of three articles, originally written in German, by Wilhelm Magnus (1907--1990). The articles are from 1930, 1931, and 1932, respectively, and were the first articles published on one-relator group theory. The first article gives a proof of the famous Freiheitssatz, and many applications of the same. The second investigates various topics in combinatorial group theory, including determining the automorphism group of the figure-eight knot group, listing the subgroups of the modular group, and a proof of the decidability of the word problem in a restricted class of one-relator groups. The third gives a proof of the decidability of the word problem in all one-relator groups. A short preface is provided, summarizing the articles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18248 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Three articles on one-relator groups by Wilhelm Magnus Nyberg-Brodda, Carl-Fredrik Group Theory History and Overview This is an English translation of three articles, originally written in German, by Wilhelm Magnus (1907--1990). The articles are from 1930, 1931, and 1932, respectively, and were the first articles published on one-relator group theory. The first article gives a proof of the famous Freiheitssatz, and many applications of the same. The second investigates various topics in combinatorial group theory, including determining the automorphism group of the figure-eight knot group, listing the subgroups of the modular group, and a proof of the decidability of the word problem in a restricted class of one-relator groups. The third gives a proof of the decidability of the word problem in all one-relator groups. A short preface is provided, summarizing the articles. |
| title | Three articles on one-relator groups by Wilhelm Magnus |
| topic | Group Theory History and Overview |
| url | https://arxiv.org/abs/2501.18248 |