One-relator quotients of free products
Published online by Cambridge University Press: 24 October 2008
Extract
Let I be a set with |I| > 1, let Hi(i ∈ I) be nontrivial groups and let H = *i ∈ IHi be their free product. Let R be a cyclically reduced element of Hi and write
if G is (isomorphic to) H/{R}H.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 88 , Issue 2 , September 1980 , pp. 233 - 243
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- Copyright © Cambridge Philosophical Society 1980
References
REFERENCES
(1)Baumslag, B.Residually free groups. Proc. London Math. Soc. 17 (1967), 402–418.CrossRefGoogle Scholar
(2)Baumslag, G.Residually finite one-relator groups. Bull. Amer. Math. Soc. 73 (1967), 618–620.CrossRefGoogle Scholar
(3)Gerstenhaber, M. and Rothaus, O. S.The solution of sets of equations in groups. Proc. Nat. Acad. Sci. U.S.A. 48 (1962), 1531–1533.CrossRefGoogle ScholarPubMed
(4)Gildenhuys, D.A generalization of Lyndon's theorem on the cohomology of one-relator groups. Canad. J. Math. 28 (1976), 473–480.CrossRefGoogle Scholar
(5)Greendlinger, M. D.On Dehn's algorithms for the conjugacy and word problems with applications. Comm. Pure Appl. Math. 13 (1960), 641–677.CrossRefGoogle Scholar
(6)Gurevich, G. A.On the conjugacy problem for groups with one defining relator. Soviet Math. Dokl. 13 (1972), 1436–1439.Google Scholar
(7)Levin, F.Solutions of equations over groups. Bull. Amer. Math. Soc. 68 (1962), 603–604.CrossRefGoogle Scholar
(8)Lewin, J. and Lewin, T.An embedding of the group algebra of a torsion-free one-relator group in a field. J. Algebra 52 (1978), 39–74.CrossRefGoogle Scholar
(10)Lyndon, R. and Schupp, P. E.Combinatorial group theory. (Springer-Verlag, Berlin, New York, Heidelberg, 1977).Google Scholar
(11)Magnus, W.Über diskontinuierliche Gruppen mit einer definierenden Relation (Der Freiheitssatz). J. Reine Angew. Math. 163 (1930), 141–165.CrossRefGoogle Scholar
(12)Magnus, W., Karrass, A. and Solitar, D.Combinatorial group theory (Dover, New York 1976).Google Scholar
(13)Newman, B. B.Some results on one-relator groups. Bull. Amer. Math. Soc. 74 (1968), 568–571.CrossRefGoogle Scholar
(14)Rothaus, O. S.On the non-triviality of some group extensions given by generators and relations. Ann. of Math. 106 (1977), 599–612.CrossRefGoogle Scholar
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