Skip to main content Accessibility help
×
Home

Some infinitely based varieties of groups

  • Roger M. Bryant (a1)

Extract

Problem 11 of Hanna Neumann's book [3] asks whether the product variety Β4Β2 has a finite basis for its laws. (For any positive integer k, Βk denotes the variety of all groups of exponent diving k.) I think that Β4Β2 was being suggested as a plausible canditate for a variety without the finite basis property; of course, at a time when no such example was known. It is the primary object of this note to verify the fact that Β4Β2 is not finitely based. Β4Β2 provides, therefore, probably the simplest example known at present of a variety which is not finitely based.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Some infinitely based varieties of groups
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Some infinitely based varieties of groups
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Some infinitely based varieties of groups
      Available formats
      ×

Copyright

References

Hide All
[1]Brooks, M. S., Kov´cs, L. G., and Newman, M. F., ‘A finite basis theorem for product varieties of groups’, Bull. Austral. Math. Soc. 2 (1970), 3944.
[2]Kov´cs, L. G., ‘On the number of varieties of groups’, J. Austral. Math. Soc. 8 (1968), 444446.
[3]Neumann, Hanna, Varieties of Groups (Springer-Verlag, Berlin, 1967).
[4]Newman, M. F., ‘Just non-finitely-based varieties of groups’, Bull. Austral. Math. Soc. 4 (1971), 343348.
[5]Vaughan-Lee, M. R., ‘Uncountably many varieties of groups’, Bull. London. Math. Soc. 2 (1970), 280286.
[6]Vaughan-Lee, M. R., ‘On product varieties of groups’, Bull. Austral. Math. Soc. 5 (1971), 239240.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Some infinitely based varieties of groups

  • Roger M. Bryant (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.