On one-relator groups having elements of finite order

Fischer, J.; Karrass, A.; Solitar, D.

doi:10.1090/S0002-9939-1972-0311780-0

On one-relator groups having elements of finite order
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by J. Fischer, A. Karrass and D. Solitar

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

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

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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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