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Counterexamples to Two Problems on One-Relator Groups

Published online by Cambridge University Press:  20 November 2018

J. Fischer
J. Fischer*
Affiliation:
Department of Computer ScienceConcordia University1455 De Maisonneuve, W. Montreal, Quebec, CanadaH3G 1M8
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In [2] G. Baumslag presents a list of twenty-three unsolved problems on one-relator groups. We give counterexamples to two of them.

Problem 5 asks whether a maximal locally free subgroup of a one-relator group always has finite “rank” (G has “rank” k if each finitely generated subgroup of G is contained in a k-generator subgroup of G).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 3 , 01 September 1976 , pp. 363 - 364
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Auslander, M. and Lyndon, R. C., Commutator subgroups of free groups, Amer. J. Math. 77 (1955), 929–931.Google Scholar
2. Baumslag, G., Some problems on one-relator groups, Springer Lecture Notes, Vol. 372, 75–81.Google Scholar
3. Burns, R. G., The finitely generated subgroups of an amalgamated product of two groups, Trans. A.M.S. 169 (1972), 293–306.Google Scholar
4. Hoare, A. H. M., Karrass, A. and Solitar, D., Subgroups of finite index in Fuchsian groups, Math. Z. 120 (1971), 289–298.Google Scholar
5. Hoare, A. H. M., Karrass, A. and D. Solitar, Subgroups of infinite index in Fuchsian groups, Math. Z. 125 (1972), 59–69.Google Scholar
6. Magnus, W., Karrass, A. and Solitar, D., Combinatorial Group Theory, Interscience, 1975.Google Scholar
7. Stallings, J., On torsion-free groups with infinitely many ends, Ann. of Math. 88 (1968), 312–334.Google Scholar