On one-relator groups having elements of finite order

Authors:
J. Fischer, A. Karrass and D. Solitar

Journal:
Proc. Amer. Math. Soc. **33** (1972), 297-301

MSC:
Primary 20F05

DOI:
https://doi.org/10.1090/S0002-9939-1972-0311780-0

MathSciNet review:
0311780

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *G* be a one-relator group having torsion. It is easy to show that there exists a normal subgroup *N* which is of finite index and torsion-free. We prove that *N* is free iff *G* is the free product of a free group and a finite cyclic group; *N* is a proper free product iff *G* is a proper free product of a free group and a one-relator group. In the proof, use is made of the following result: the elements of finite order in *G* generate a group which is the free product of conjugates of a finite cyclic group.

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DOI:
https://doi.org/10.1090/S0002-9939-1972-0311780-0

Keywords:
One-relator groups,
free products

Article copyright:
© Copyright 1972
American Mathematical Society