Three articles on one-relator groups by Wilhelm Magnus

2025/01/30 by Nyberg-Brodda, Carl-Fredrik
#FOS: Mathematics #Group Theory (math.GR) #History and Overview (math.HO)

paper · doi:10.48550/arxiv.2501.18248

Abstract

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.

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