Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-20T04:36:18.771Z Has data issue: false hasContentIssue false
  • English
  • Français

One-relator quotients of free products

Published online by Cambridge University Press:  24 October 2008

Stephen J. Pride
Stephen J. Pride
Affiliation:
University of Glasgow
Get access Rights & Permissions [Opens in a new window]

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
Copyright
Copyright © Cambridge Philosophical Society 1980

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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
(9)Lyndon, R.On the Freiheitssatz. J. London Math. Soc. 5 (1972), 95–101.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
(15)Schupp, P. E.A strengthened Freiheitssatz. Math. Ann. 221 (1976), 73–80.CrossRefGoogle Scholar