Skip to main content

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 372))

Abstract

The isomorphism problem is perhaps the most important as well as the most intractable problem in the theory of 1-relator groups. Almost nothing is known besides Magnus’ Theorem [16]:

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Benjamin Baumslag, “Residually free groups”, Proc. London Math. Soc. (3) 17 (1967), 402–418. MR356738.

    Google Scholar 

  2. Benjamin Baumslag, “Generalized free products whose two-generator subgroups are free”, J. London Math. Soc. 43 (1968), 601–606. MR3802217.

    Google Scholar 

  3. Gilbert Baumslag, “On generalised free products”, Math. Z. 78 (1962), 423–438. MR253980.

    Google Scholar 

  4. Gilbert Baumslag, “On the residual finiteness of generalised free products of nilpotent groups”, Trans. Are r. Math. Soc. 106 (1963), 192–209. MR262489.

    Google Scholar 

  5. Gilbert Baumslag, “Groups with one defining relator”, J. Austral. Math. Soc. 4 (1964), 385–392. MR303124.

    Google Scholar 

  6. Gilbert Baumslag, “A non-cyclic one-relator group all of whose finite quotients are cyclic”, J. Austral. Math. Soc. 10 (1969), 497–498. MR407337.

    Google Scholar 

  7. Gilbert Baumslag, “Groups with the same lower central sequence as a relatively free group. II. Properties”, Trans. Amer. Math. Soc. 142 (1969), 507–538. Múí396959.

    Google Scholar 

  8. Gilbert Baumslag, “Positive one-relator groups”, Trans. Amer. Math. Soc. 156 (1971), 165–183. 118438325.

    Google Scholar 

  9. Gilbert Baumslag, “Finitely generated cyclic extensions of free groups are residually finite”, Bull. Austral. Math. Suc. 5 (1971), 87–94. Zb1.216.83.

    Google Scholar 

  10. Gilbert Baumslag, “One-relator metabelian groups”, unpublished.

    Google Scholar 

  11. R.G. Burns, “On the finitely generated subgroups of an amalgamated product of two groups”, Trans. Amer. Math. Soc. 169 (1972), 293–306.

    Google Scholar 

  12. I.M.S. Dey, “Schreier systems in free products”, Proc. Glasgow Math. Assoc. 7 (1965–66), 61–79. MR325718.

    Google Scholar 

  13. M.J. Dunwoody, Review of “More groups that are just about free” by Gilbert Baumslag, (Pull. Amer. Math. Soc. 74 (1968), 752–754), in MR371449.

    Google Scholar 

  14. Marshall Hall, Jr., “Subgroups of finite index in free groups”, Gonad. J. Math. 1 (1949), 187-190. MR10,506.

    Google Scholar 

  15. A. Karrass and D. Solitar, “The subgroups of a free product of two groups with an amalgamated subgroup”, Trans. Amer. Math. Soc. 150 (1970), 227–255. 415499.

    Google Scholar 

  16. W. Magnus, “Über freie Faktorgruppen und freie Untergruppen gegebener Gruppen”, Monatah. Math. Phys. 47 (1939), 307–313. FdM65,59.

    Google Scholar 

  17. W. Magnus, “Rational representations of Fuchsian groups”, these Proc.

    Google Scholar 

  18. Stephen Meskin, “On some groups with a single defining relator”, Math. Ann. 184 (1969), 193–196 (1970). MR411848.

    Google Scholar 

  19. B.B. Newman, “Some results on one-relator groups”, Bonn. Amer. Math. Soc. 74 (1968), 568–571. MR365204.

    Google Scholar 

  20. B.A.F. Wehrfritz, “Generalized free products of linear groups”, Proc. London Math. Soc. (3) 27 (1973), 402–424.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1974 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Baumslag, G. (1974). Some Problems on One-Relator Groups. In: Newman, M.F. (eds) Proceedings of the Second International Conference on the Theory of Groups. Lecture Notes in Mathematics, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21571-5_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-21571-5_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06845-7

  • Online ISBN: 978-3-662-21571-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics