Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-06-04T04:18:49.667Z Has data issue: false hasContentIssue false
  • English
  • Français

On decomposable varieties of groups

Published online by Cambridge University Press:  09 April 2009

John Cossey
John Cossey
Affiliation:
Department of Pure MathematicsSchool of General StudiesThe Australian National UniversityCanberra
Rights & Permissions [Opens in a new window]

Extract

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 shall be concerned with problem 7 of Hanna Neumann [7], which asks: Prove or disprove that if U and B are varieties, and neither of U and B is contained in the other, then U ∪ B and [U, B] are decomposable if and only if U and B have a common non-trivial right hand factor.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 3 , August 1970 , pp. 340 - 342
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Brumberg, N., ‘On the mutual commutator variety of two varieties’, Summary of scientific contributions, Ninth All-Union Algebraic Colloquium, July 1968, 31–33 (in Russian).CrossRefGoogle Scholar
[2]Cossey, John, ‘Some classes of indecomposable varieties of groups’, to appear in J. Australian Math. Soc.Google Scholar
[3]Dunwoody, M. J., ‘On product varieties’, Math. Zeitschrift 104 (1968), 91–97.CrossRefGoogle Scholar
[4]Huppert, B., Endliche Gruppen, I, (Die Grundlehren der Mathematischen Wissenschaften, Bd 134, Springer-Verlag, Berlin, 1967).CrossRefGoogle Scholar
[5]Kovács, L. G. and Newman, M. F., ‘On critical groups’, J. Australian Math. Soc. 4 (1966), 237–250.Google Scholar
[6]Kurosh, A. G., The theory of groups, Vol. 2 (Chelsea, New York, 1960).Google Scholar
[7]Neumann, Hanna, Varieties of groups (Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd 37, Springer Verlag, Berlin, 1967.)CrossRefGoogle Scholar
[8]Oates, Sheila, ‘Identical relations in groups’, J. London Math. Soc. 38 (1963), 71–78.Google Scholar
[9]Weichsel, P. M., A decomposition theory for finite groups with applications to p-groups’, Trans. Amer. Math. Soc. 102 (1962), 218–226.Google Scholar