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In 1932, while working on the word problem for groups, Magnus showed that groups with one relation always have a decidable word problem.
Magnus was a faculty member in Frankfurt from 1933 until 1938. He refused to join the Nazi Party and, as a consequence, was not allowed to hold an academic post during World War II. In 1947 he became a professor at the University of Göttingen.
with Gilbert Baumslag and Bruce Chandler, eds.: Wilhelm Magnus, Collected Papers. Springer-Verlag 1984.
Noneuclidean tessellations and their groups. Academic Press 1974.
with Bruce Chandler: The History of Combinatorial Group Theory. A Case Study in the History of Ideas. Springer 1982.
Wilhelm Magnus, Abraham Karrass, Donald Solitar, Combinatorial group theory. Presentations of groups in terms of generators and relations, Reprint of the 1976 second edition, Dover Publications, Inc., Mineola, NY, 2004. ISBN0-486-43830-9
Wilhelm Magnus, Stanley Winkler, Hill's equation, Reprint of the 1979 second edition, Dover Publications, Inc., Mineola, NY, 2004. ISBN0-486-49565-5.
with Israel Grossman: Groups and their Graphs. Random House (New Mathematical Library 14) 1965.
Wilhelm Magnus, Fritz Oberhettinger, and Raz Pal Soni, Formulas and Theorems for the Special Functions of Mathematical Physics. Springer-Verlag New York Inc., New York, 1966.
with Fritz Oberhettinger: Formeln und Lehrsätze für die speziellen Funktionen der mathematischen Physik. Springer 1943; 2nd edition, 1948; 3rd edition in English, Formulas and theorems for the functions of mathematical physics, Chelsea Pub. Co. 1966.
with Fritz Oberhettinger: Anwendungen der elliptischen Funktionen in Physik und Technik. Springer 1949.