Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-06-08T12:02:28.076Z Has data issue: false hasContentIssue false

Multiplicators and metabelian groups

Published online by Cambridge University Press:  09 April 2009

Gilbert Brumslag
Affiliation:
City College of the City University of New York, Convent Avenue at 138th Street, New York, U.S.A.
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 prove here that the multiplicator of certain simply described metabelian groups is not finitely generated

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1976

References

Baumslag, Gilbert (1969), ‘Groups with the same lower central sequence as a relatively free group. II. Properties’, Trans. Amer. Math. S⊙c. 142, 507538.CrossRefGoogle Scholar
Baumslag, Gilbert (1971), ‘A finitely generated infinitely related group with trivial multiplicator’, Bull. Austral. Math. Soc. 5, 131136.CrossRefGoogle Scholar
Baumslag, Gilbert (1972), ‘Some remarks about multiplicators and finitely presented groups’, Math. Z. 126, 239242.CrossRefGoogle Scholar
Baumslag, Gilbert (1974), ‘Finitely presented metabelian groups’, Proc. Second Internal. Conf. Theory of Groups, Canberra, 1973, 6574 (Lecture Notes in Mathematics, 372, Springer-Verlag, Berlin, Heidelberg, New York).CrossRefGoogle Scholar
Baumslag, Gilbert and Strebel, Ralph (in press), ‘Some finitely generated, infinitely related metabelian groups with trivial multiplicator’, J. Algebra.Google Scholar
Bousfield, A. K. and Kan, D. (1971), ‘Homotopy Limits, Completions and Localizations’, (Lecture Notes in Mathematics 249, Springer-Verlag, Berlin, Heidelberg, New York).CrossRefGoogle Scholar
Gupta, C. K. (1969), ‘A faithful matrix representation for certain centre-by-metabelian groups’, J. Austral. Math. Soc. 10, 451464.CrossRefGoogle Scholar
PeMecлeyHHIОБ, B. H. [Remeslennikov, V. N.] (1969), пpeдctaБлeнИэe Конeчно порождeннъIх MeTaбeлэBжиж Гρупп MaτρHцаmн- [Representaion of finitely generated metabelian groups by matrices], Algebra i Loġika 8, 7275;Google Scholar
Algebra and Logic 8, 3940.CrossRefGoogle Scholar
SШмэББкиш, A. Л. [Šmel'kin, A. L.] (1965), ‘O pазрэшимьі произбэ гρяпп’ [On soluble products of groups], Sibirsk. Mat. Ž. 6, 212220.Google Scholar