Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-28T06:13:08.153Z Has data issue: false hasContentIssue false
  • English
  • Français

On varieties of soluble groups

Published online by Cambridge University Press:  17 April 2009

J.R.J. Groves
J.R.J. Groves
Affiliation:
Department of Mathematics, Institute of Advanced Studies, The Australian National University, Canberra, ACT.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that, under certain conditions, a soluble variety of groups which does not contain the variety of all metabelian groups is a finite exponent by nilpotent by finite exponent variety.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 1 , August 1971 , pp. 95 - 109
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Bryce, R.A., “Metabelian groups and varieties”, Philos. Trans. Roy. Soc. London Ser. A 266 (1970), 281–355.Google Scholar
[2]Gupta, Narain, “On metanilpotent varieties of groups”, Canad. J. Math. 22 (1970), 875–877.CrossRefGoogle Scholar
[3]Hall, P., “Some sufficient conditions for a group to be nilpotent”, Illinois J. Math. 2 (1958), 787–801.CrossRefGoogle Scholar
[4]Higman, Graham, “Some remarks on varieties of groups”, Quart. J. Math. Oxford (2) 10 (1959), 165–178.CrossRefGoogle Scholar
[5]Kovács, L.G. and Newman, M.F., “On non-Cross varieties of groups”, J. Austral. Math. Soc. 12 (1971), 129–144.CrossRefGoogle Scholar
[6]Neumann, B.H., “Groups with finite classes of conjugate elements”, Proc. London Math. Soc. (3) 1 (1951), 178–187.CrossRefGoogle Scholar
[7]Neumann, Hanna, Varieties of groups (Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 37, Springer-Verlag, Berlin, Heidelbe Heidelberg, New York, 1907).Google Scholar
[8]Neumann, Peter M., “A note on the direct decomposability of relatively free groups”, Quart. J. Math. Oxford (2) 19 (1968), 67–79.CrossRefGoogle Scholar
[9]Robinson, Derek J.S., Infinite soluble and nilpotent groups (Queen Mary College Mathematics Hotes, London, H.D. [1968]).Google Scholar
[10]Šmel'kin, A.L., “On soluble group varieties”, Soviet Math. Dokl. 9 (1968), 100–103.Google Scholar