×

zbMATH — the first resource for mathematics

On Andrews-Curtis conjectures for soluble groups. (English) Zbl 06850905
MSC:
20F05 Generators, relations, and presentations of groups
20F16 Solvable groups, supersolvable groups
Software:
MathOverflow
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Andrews, J. J.; Curtis, M. L., Free groups and handlebodies, Proc. Am. Math. Soc., 16, 192-195, (1965) · Zbl 0131.38301
[2] Andrews, J. J.; Curtis, M. L., Extended Nielsen operations in free groups, Am. Math. Mon., 73, 21-28, (1966) · Zbl 0135.04403
[3] Baer, R., Der reduzierte rang einer gruppe, J. Reine Angew. Math., 214/215, 146-173, (1964) · Zbl 0125.28603
[4] Borovik, A. V.; Lubotzky, A.; Myasnikov, A. G., Infinite Groups: Geometric, Combinatorial and Dynamical Aspects, 248, The finitary Andrews-Curtis conjecture, 15-30, (2005), Birkhäuser, Basel · Zbl 1114.20011
[5] M. Bridson, The complexity of balanced presentations and the Andrews-Curtis conjecture, arXiv:1504.04187 [math.GR], April (2015).
[6] Burns, R. G.; Herfort, W. N.; Kam, S.-M.; Macedońska, O.; Zalesskii, P. A., Recalcitrance in groups, Bull. Aust. Math. Soc., 60, 2, 245-251, (1999) · Zbl 0938.20026
[7] Burns, R. G.; Macedońska, O., Balanced presentations of the trivial group, Bull. Lond. Math. Soc., 25, 6, 513-526, (1993) · Zbl 0796.20022
[8] Burns, R. G.; Oancea, D., Recalcitrance in groups II, J. Group Theory, 15, 1, 101-117, (2012) · Zbl 1245.20031
[9] Diaconis, P.; Graham, R., The graph of generating sets of an abelian group, Colloq. Math., 80, 1, 31-38, (1999) · Zbl 0949.60012
[10] Dlab, V.; Kořínek, V., The Frattini subgroup of a direct product of groups, Czech. Math. J., 10, 85, 350-358, (1960) · Zbl 0101.26303
[11] D. Francoeur and A. Garrido, Maximal subgroups of groups of intermediate growth, arXiv:1611.01216 [math.GR]. · Zbl 06975521
[12] González-Acuna, F., Homomorphs of knot groups, Ann. Math. (2), 102, 2, 373-377, (1975) · Zbl 0323.57010
[13] L. Guyot, Generators of split extensions of Abelian groups by cyclic groups, arXiv:1604.08896 [math.GR]. · Zbl 1456.20028
[14] Havas, G.; Ramsay, C., Breadth-first search and the Andrews-Curtis conjecture, Int. J. Algebr. Comput., 13, 1, 61-68, (2003) · Zbl 1059.20029
[15] Hillman, J. A., Geometry & Topology Monographs, 5, Four-manifolds, geometries and knots, (2002), Geometry & Topology Publications, Coventry · Zbl 1087.57015
[16] Hillman, J. A., 2-knots with solvable groups, J. Knot Theory Ramifications, 20, 7, 977-994, (2011) · Zbl 1225.57014
[17] Kappe, W. P.; Parker, D. B., Elements with trivial centralizer in wreath products, Trans. Am. Math. Soc., 150, 201-212, (1970) · Zbl 0216.08801
[18] Lennox, J. C.; Wiegold, J., Generators and killers for direct and free products, Arch. Math. (Basel), 34, 4, 296-300, (1980) · Zbl 0447.20029
[19] B. Lishak, Balanced finite presentations of the trivial group, arXiv:1504.00418 [math.GR]. · Zbl 1405.20022
[20] Lyndon, R.; Schupp, P., Combinatorial Group Theory, (1977), Springer-Verlag, Berlin
[21] Myasnikov, A. G., Extended Nielsen transformations and the trivial group, Mat. Zametki, 35, 4, 491-495, (1984)
[22] A. Myropolska, The class \(M N\) of groups in which all maximal subgroups are normal, arXiv:1509.08090 [math.GR]. · Zbl 1412.20015
[23] Myropolska, A., Andrews-Curtis and Nielsen equivalence relations on some infinite groups, J. Group Theory, 19, 1, 161-178, (2016) · Zbl 1339.20026
[24] Oancea, D., A note on Nielsen equivalence in finitely generated abelian groups, Bull. Aust. Math. Soc., 84, 1, 127-136, (2011) · Zbl 1233.20029
[25] Oancea, D., Coessential abelianization morphisms in the category of groups, Can. Math. Bull., 56, 2, 395-399, (2013) · Zbl 1279.20040
[26] Ol’shanskiĭ, A. Y., Geometry of Defining Relations in Groups, 70, (1991), Kluwer Academic Publishers Group, Dordrecht
[27] I. Pak, What do we know about the product replacement algorithm? in Groups and computation, III (Columbus, OH, 1999), Ohio State Univ. Math. Res. Inst. Publ., Vol. 8 (de Gruyter, Berlin, 2001), pp. 301-347. · Zbl 0986.68172
[28] Plotnick, S. P., Infinitely many disk knots with the same exterior, Math. Proc. Camb. Philos. Soc., 93, 1, 67-72, (1983) · Zbl 0522.57016
[29] Shelah, S., On a problem of kurosh, Jónsson groups, and applications, Word problems, II (Conf. on Decision Problems in Algebra, Oxford, 1976), 95, 373-394, (1980), North-Holland, Amsterdam-New York
[30] Silver, D. S.; Whitten, W.; Williams, S. G., Knot groups with many killers, Bull. Aust. Math. Soc., 81, 3, 507-513, (2010) · Zbl 1194.57013
[31] Weiss, E., Algebraic Number Theory, (1998), Dover Publications Inc., Mineola, NY
[32] Wright, P., Group presentations and formal deformations., Trans. Am. Math. Soc., 208, 161-169, (1975) · Zbl 0318.57010
[33] zcn (http://mathoverflow.net/users/44201/zcn). When does a ring surjection imply a surjection of the group of units? MathOverflow. URL:http://mathoverflow.net/q/153526 (version: 2014-01-03).
[34] Zeeman, E. C., On the dunce hat, Topology, 2, 341-358, (1964) · Zbl 0116.40801
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.