Counterexamples to Two Problems on One-Relator Groups
Canadian mathematical bulletin, Tome 19 (1976) no. 3, pp. 363-364

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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).
Fischer, J. Counterexamples to Two Problems on One-Relator Groups. Canadian mathematical bulletin, Tome 19 (1976) no. 3, pp. 363-364. doi: 10.4153/CMB-1976-055-2
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[1] 1. Auslander, M. and Lyndon, R. C., Commutator subgroups of free groups, Amer. J. Math. 77 (1955), 929–931. Google Scholar

[2] 2. Baumslag, G., Some problems on one-relator groups, Springer Lecture Notes, Vol. 372, 75–81. Google Scholar

[3] 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] 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] 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] 6. Magnus, W., Karrass, A. and Solitar, D., Combinatorial Group Theory, Interscience, 1975. Google Scholar

[7] 7. Stallings, J., On torsion-free groups with infinitely many ends, Ann. of Math. 88 (1968), 312–334. Google Scholar

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