One-relator group (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "One-relator group" in English language version.

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27ams.org

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7semanticscholar.org

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ams.org

mathscinet.ams.org

Magnus, Wilhelm (1930). "Über diskontinuierliche Gruppen mit einer definierenden Relation. (Der Freiheitssatz)". Journal für die reine und angewandte Mathematik. 1930 (163): 141–165. doi:10.1515/crll.1930.163.141. MR 1581238. S2CID 117245586.
Lyndon, Roger C. (1972). "On the Freiheitssatz". Journal of the London Mathematical Society. Second Series. 5: 95–101. doi:10.1112/jlms/s2-5.1.95. hdl:2027.42/135658. MR 0294465.
Weinbaum, C. M. (1972). "On relators and diagrams for groups with one defining relation". Illinois Journal of Mathematics. 16 (2): 308–322. doi:10.1215/ijm/1256052287. MR 0297849.
Fischer, J.; Karrass, A.; Solitar, D. (1972). "On one-relator groups having elements of finite order". Proceedings of the American Mathematical Society. 33 (2): 297–301. doi:10.2307/2038048. JSTOR 2038048. MR 0311780.
Dyer, Eldon; Vasquez, A. T. (1973). "Some small aspherical spaces". Journal of the Australian Mathematical Society. 16 (3): 332–352. doi:10.1017/S1446788700015147. MR 0341476.
Shenitzer, Abe (1955). "Decomposition of a group with a single defining relation into a free product". Proceedings of the American Mathematical Society. 6 (2): 273–279. doi:10.2307/2032354. JSTOR 2032354. MR 0069174.
Howie, James (1980). "On locally indicable groups". Mathematische Zeitschrift. 182 (4): 445–461. doi:10.1007/BF01214717. MR 0667000. S2CID 121292137.
Murasugi, Kunio (1964). "The center of a group with a single defining relation". Mathematische Annalen. 155 (3): 246–251. doi:10.1007/BF01344162. MR 0163945. S2CID 119454184.
Magnus, Wilhelm (1931). "Untersuchungen über einige unendliche diskontinuierliche Gruppen". Mathematische Annalen. 105 (1): 52–74. doi:10.1007/BF01455808. MR 1512704. S2CID 120949491.
Gilbert Baumslag; Donald Solitar (1962). "Some two-generator one-relator non-Hopfian groups". Bulletin of the American Mathematical Society. 68 (3): 199–201. doi:10.1090/S0002-9904-1962-10745-9. MR 0142635.
Chebotarʹ, A.A. (1971). "Subgroups of groups with one defining relation that do not contain free subgroups of rank 2" (PDF). Algebra i Logika. 10 (5): 570–586. MR 0313404.
Cohen, Daniel E.; Lyndon, Roger C. (1963). "Free bases for normal subgroups of free groups". Transactions of the American Mathematical Society. 108 (3): 526–537. doi:10.1090/S0002-9947-1963-0170930-9. MR 0170930.
Karrass, A.; Magnus, W.; Solitar, D. (1960). "Elements of finite order in groups with a single defining relation". Communications on Pure and Applied Mathematics. 13: 57–66. doi:10.1002/cpa.3160130107. MR 0124384.
Newman, B. B. (1968). "Some results on one-relator groups". Bulletin of the American Mathematical Society. 74 (3): 568–571. doi:10.1090/S0002-9904-1968-12012-9. MR 0222152.
Howie, James (1984). "Cohomology of one-relator products of locally indicable groups". Journal of the London Mathematical Society. 30 (3): 419–430. doi:10.1112/jlms/s2-30.3.419. MR 0810951.
Baumslag, Gilbert; Fine, Benjamin; Rosenberger, Gerhard (2019). "One-relator groups: an overview". Groups St Andrews 2017 in Birmingham. London Math. Soc. Lecture Note Ser. Vol. 455. Cambridge University Press. pp. 119–157. ISBN 978-1-108-72874-4. MR 3931411.
Louder, Larsen; Wilton, Henry (2020). "One-relator groups with torsion are coherent". Mathematical Research Letters. 27 (5): 1499–1512. arXiv:1805.11976. doi:10.4310/MRL.2020.v27.n5.a9. MR 4216595. S2CID 119141737.
Dahmani, Francois; Guirardel, Vincent (2011). "The isomorphism problem for all hyperbolic groups". Geometric and Functional Analysis. 21 (2): 223–300. arXiv:1002.2590. doi:10.1007/s00039-011-0120-0. MR 2795509.
Wise, Daniel T. (2009). "Research announcement: the structure of groups with a quasiconvex hierarchy". Electronic Research Announcements in Mathematical Sciences. 16: 44–55. doi:10.3934/era.2009.16.44. MR 2558631.
Moldavanskii, D.I. (1967). "Certain subgroups of groups with one defining relation". Siberian Mathematical Journal. 8: 1370–1384. doi:10.1007/BF02196411. MR 0220810. S2CID 119585707.
Brown, Kenneth S. (1987). "Trees, valuations, and the Bieri-Neumann-Strebel invariant". Inventiones Mathematicae. 90 (3): 479–504. Bibcode:1987InMat..90..479B. doi:10.1007/BF01389176. MR 0914847. S2CID 122703100., Theorem 4.3
Dunfield, Nathan; Thurston, Dylan (2006). "A random tunnel number one 3–manifold does not fiber over the circle". Geometry & Topology. 10 (4): 2431–2499. arXiv:math/0510129. doi:10.2140/gt.2006.10.2431. MR 2284062., Theorem 6.1
Gersten, S. M. (1987). "Nonsingular equations of small weight over groups". Combinatorial group theory and topology (Alta, Utah, 1984). Annals of Mathematics Studies. Vol. 111. Princeton University Press. pp. 121–144. doi:10.1515/9781400882083-007. ISBN 0-691-08409-2. MR 0895612.
Klyachko, A. A. (1993). "A funny property of sphere and equations over groups". Communications in Algebra. 21 (7): 2555–2575. doi:10.1080/00927879308824692. MR 1218513.
John R. Stallings (1968). "Groups of dimension 1 are locally free". Bulletin of the American Mathematical Society. 74 (2): 361–364. doi:10.1090/S0002-9904-1968-11955-X. MR 0223439.
Baumslag, Gilbert; Fine, Benjamin; Miller, Charles F. III; Troeger, Douglas (2009). "Virtual properties of cyclically pinched one-relator groups". International Journal of Algebra and Computation. 19 (2): 213–227. doi:10.1142/S0218196709005032. MR 2512551.
Baumslag, Gilbert; Troeger, Douglas (2008). "Virtually free-by-cyclic one-relator groups. I.". Aspects of infinite groups. Algebra and Discrete Mathematics. Vol. 1. World Scientific Publishing. ISBN 978-981-279-340-9. MR 2571508.

arxiv.org

Louder, Larsen; Wilton, Henry (2020). "One-relator groups with torsion are coherent". Mathematical Research Letters. 27 (5): 1499–1512. arXiv:1805.11976. doi:10.4310/MRL.2020.v27.n5.a9. MR 4216595. S2CID 119141737.
Dahmani, Francois; Guirardel, Vincent (2011). "The isomorphism problem for all hyperbolic groups". Geometric and Functional Analysis. 21 (2): 223–300. arXiv:1002.2590. doi:10.1007/s00039-011-0120-0. MR 2795509.
Dunfield, Nathan; Thurston, Dylan (2006). "A random tunnel number one 3–manifold does not fiber over the circle". Geometry & Topology. 10 (4): 2431–2499. arXiv:math/0510129. doi:10.2140/gt.2006.10.2431. MR 2284062., Theorem 6.1

books.google.com

Baumslag, Gilbert; Fine, Benjamin; Rosenberger, Gerhard (2019). "One-relator groups: an overview". Groups St Andrews 2017 in Birmingham. London Math. Soc. Lecture Note Ser. Vol. 455. Cambridge University Press. pp. 119–157. ISBN 978-1-108-72874-4. MR 3931411.

degruyter.com

Gersten, S. M. (1987). "Nonsingular equations of small weight over groups". Combinatorial group theory and topology (Alta, Utah, 1984). Annals of Mathematics Studies. Vol. 111. Princeton University Press. pp. 121–144. doi:10.1515/9781400882083-007. ISBN 0-691-08409-2. MR 0895612.

doi.org

Magnus, Wilhelm (1930). "Über diskontinuierliche Gruppen mit einer definierenden Relation. (Der Freiheitssatz)". Journal für die reine und angewandte Mathematik. 1930 (163): 141–165. doi:10.1515/crll.1930.163.141. MR 1581238. S2CID 117245586.
Lyndon, Roger C. (1972). "On the Freiheitssatz". Journal of the London Mathematical Society. Second Series. 5: 95–101. doi:10.1112/jlms/s2-5.1.95. hdl:2027.42/135658. MR 0294465.
Weinbaum, C. M. (1972). "On relators and diagrams for groups with one defining relation". Illinois Journal of Mathematics. 16 (2): 308–322. doi:10.1215/ijm/1256052287. MR 0297849.
Fischer, J.; Karrass, A.; Solitar, D. (1972). "On one-relator groups having elements of finite order". Proceedings of the American Mathematical Society. 33 (2): 297–301. doi:10.2307/2038048. JSTOR 2038048. MR 0311780.
Dyer, Eldon; Vasquez, A. T. (1973). "Some small aspherical spaces". Journal of the Australian Mathematical Society. 16 (3): 332–352. doi:10.1017/S1446788700015147. MR 0341476.
Shenitzer, Abe (1955). "Decomposition of a group with a single defining relation into a free product". Proceedings of the American Mathematical Society. 6 (2): 273–279. doi:10.2307/2032354. JSTOR 2032354. MR 0069174.
Howie, James (1980). "On locally indicable groups". Mathematische Zeitschrift. 182 (4): 445–461. doi:10.1007/BF01214717. MR 0667000. S2CID 121292137.
Murasugi, Kunio (1964). "The center of a group with a single defining relation". Mathematische Annalen. 155 (3): 246–251. doi:10.1007/BF01344162. MR 0163945. S2CID 119454184.
Magnus, Wilhelm (1931). "Untersuchungen über einige unendliche diskontinuierliche Gruppen". Mathematische Annalen. 105 (1): 52–74. doi:10.1007/BF01455808. MR 1512704. S2CID 120949491.
Gilbert Baumslag; Donald Solitar (1962). "Some two-generator one-relator non-Hopfian groups". Bulletin of the American Mathematical Society. 68 (3): 199–201. doi:10.1090/S0002-9904-1962-10745-9. MR 0142635.
Cohen, Daniel E.; Lyndon, Roger C. (1963). "Free bases for normal subgroups of free groups". Transactions of the American Mathematical Society. 108 (3): 526–537. doi:10.1090/S0002-9947-1963-0170930-9. MR 0170930.
Karrass, A.; Magnus, W.; Solitar, D. (1960). "Elements of finite order in groups with a single defining relation". Communications on Pure and Applied Mathematics. 13: 57–66. doi:10.1002/cpa.3160130107. MR 0124384.
Newman, B. B. (1968). "Some results on one-relator groups". Bulletin of the American Mathematical Society. 74 (3): 568–571. doi:10.1090/S0002-9904-1968-12012-9. MR 0222152.
Howie, James (1984). "Cohomology of one-relator products of locally indicable groups". Journal of the London Mathematical Society. 30 (3): 419–430. doi:10.1112/jlms/s2-30.3.419. MR 0810951.
Louder, Larsen; Wilton, Henry (2020). "One-relator groups with torsion are coherent". Mathematical Research Letters. 27 (5): 1499–1512. arXiv:1805.11976. doi:10.4310/MRL.2020.v27.n5.a9. MR 4216595. S2CID 119141737.
Dahmani, Francois; Guirardel, Vincent (2011). "The isomorphism problem for all hyperbolic groups". Geometric and Functional Analysis. 21 (2): 223–300. arXiv:1002.2590. doi:10.1007/s00039-011-0120-0. MR 2795509.
Wise, Daniel T. (2009). "Research announcement: the structure of groups with a quasiconvex hierarchy". Electronic Research Announcements in Mathematical Sciences. 16: 44–55. doi:10.3934/era.2009.16.44. MR 2558631.
Moldavanskii, D.I. (1967). "Certain subgroups of groups with one defining relation". Siberian Mathematical Journal. 8: 1370–1384. doi:10.1007/BF02196411. MR 0220810. S2CID 119585707.
Brown, Kenneth S. (1987). "Trees, valuations, and the Bieri-Neumann-Strebel invariant". Inventiones Mathematicae. 90 (3): 479–504. Bibcode:1987InMat..90..479B. doi:10.1007/BF01389176. MR 0914847. S2CID 122703100., Theorem 4.3
Dunfield, Nathan; Thurston, Dylan (2006). "A random tunnel number one 3–manifold does not fiber over the circle". Geometry & Topology. 10 (4): 2431–2499. arXiv:math/0510129. doi:10.2140/gt.2006.10.2431. MR 2284062., Theorem 6.1
Gersten, S. M. (1987). "Nonsingular equations of small weight over groups". Combinatorial group theory and topology (Alta, Utah, 1984). Annals of Mathematics Studies. Vol. 111. Princeton University Press. pp. 121–144. doi:10.1515/9781400882083-007. ISBN 0-691-08409-2. MR 0895612.
Klyachko, A. A. (1993). "A funny property of sphere and equations over groups". Communications in Algebra. 21 (7): 2555–2575. doi:10.1080/00927879308824692. MR 1218513.
John R. Stallings (1968). "Groups of dimension 1 are locally free". Bulletin of the American Mathematical Society. 74 (2): 361–364. doi:10.1090/S0002-9904-1968-11955-X. MR 0223439.
Baumslag, Gilbert; Fine, Benjamin; Miller, Charles F. III; Troeger, Douglas (2009). "Virtual properties of cyclically pinched one-relator groups". International Journal of Algebra and Computation. 19 (2): 213–227. doi:10.1142/S0218196709005032. MR 2512551.

handle.net

hdl.handle.net

Lyndon, Roger C. (1972). "On the Freiheitssatz". Journal of the London Mathematical Society. Second Series. 5: 95–101. doi:10.1112/jlms/s2-5.1.95. hdl:2027.42/135658. MR 0294465.

harvard.edu

ui.adsabs.harvard.edu

Brown, Kenneth S. (1987). "Trees, valuations, and the Bieri-Neumann-Strebel invariant". Inventiones Mathematicae. 90 (3): 479–504. Bibcode:1987InMat..90..479B. doi:10.1007/BF01389176. MR 0914847. S2CID 122703100., Theorem 4.3

jstor.org

Fischer, J.; Karrass, A.; Solitar, D. (1972). "On one-relator groups having elements of finite order". Proceedings of the American Mathematical Society. 33 (2): 297–301. doi:10.2307/2038048. JSTOR 2038048. MR 0311780.
Shenitzer, Abe (1955). "Decomposition of a group with a single defining relation into a free product". Proceedings of the American Mathematical Society. 6 (2): 273–279. doi:10.2307/2032354. JSTOR 2032354. MR 0069174.

nsc.ru

math.nsc.ru

Chebotarʹ, A.A. (1971). "Subgroups of groups with one defining relation that do not contain free subgroups of rank 2" (PDF). Algebra i Logika. 10 (5): 570–586. MR 0313404.

semanticscholar.org

api.semanticscholar.org

Magnus, Wilhelm (1930). "Über diskontinuierliche Gruppen mit einer definierenden Relation. (Der Freiheitssatz)". Journal für die reine und angewandte Mathematik. 1930 (163): 141–165. doi:10.1515/crll.1930.163.141. MR 1581238. S2CID 117245586.
Howie, James (1980). "On locally indicable groups". Mathematische Zeitschrift. 182 (4): 445–461. doi:10.1007/BF01214717. MR 0667000. S2CID 121292137.
Murasugi, Kunio (1964). "The center of a group with a single defining relation". Mathematische Annalen. 155 (3): 246–251. doi:10.1007/BF01344162. MR 0163945. S2CID 119454184.
Magnus, Wilhelm (1931). "Untersuchungen über einige unendliche diskontinuierliche Gruppen". Mathematische Annalen. 105 (1): 52–74. doi:10.1007/BF01455808. MR 1512704. S2CID 120949491.
Louder, Larsen; Wilton, Henry (2020). "One-relator groups with torsion are coherent". Mathematical Research Letters. 27 (5): 1499–1512. arXiv:1805.11976. doi:10.4310/MRL.2020.v27.n5.a9. MR 4216595. S2CID 119141737.
Moldavanskii, D.I. (1967). "Certain subgroups of groups with one defining relation". Siberian Mathematical Journal. 8: 1370–1384. doi:10.1007/BF02196411. MR 0220810. S2CID 119585707.
Brown, Kenneth S. (1987). "Trees, valuations, and the Bieri-Neumann-Strebel invariant". Inventiones Mathematicae. 90 (3): 479–504. Bibcode:1987InMat..90..479B. doi:10.1007/BF01389176. MR 0914847. S2CID 122703100., Theorem 4.3