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Metabelian groups and varieties

Published online by Cambridge University Press:  17 April 2009

R. A. Bryce
R. A. Bryce
Affiliation:
Department of Mathematics, IAS, The Australian National University, Canberra. A.C.T.
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Abstract

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Here we announce results which will appear in full in due course elsewhere. The aim is a study of varieties of metabelian groups. The technique is to study varieties of certain universal algebras, which are very similar to groups, called bigroups. For certain varieties of bigroups all the non-nilpotent join-irreducible subvarieties are determined, and this is used to reduce the same problem for varieties of metabelian groups to the case of prime-power exponent. Questions of distributivity of the lattice of metabelian varieties are also discussed.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 1 , April 1969 , pp. 15 - 25
Copyright
Copyright © Australian Mathematical Society 1969

References

[1] Brisley, Warren, “On varieties of metabelian p-groups and their laws”, J. Austral. Math. Soc. 7 (1967), 64–80.CrossRefGoogle Scholar
[2] Brisley, Warren, “Varieties of metabelian p-groups of class p, p + 1”, submitted J. Austral. Math. Soc.Google Scholar
[3] Brooks, M.S., “On varieties of metabelian groups of prime-power exponent”, Ph.D. Thesis, Austral. Nat. Univ., 1968.Google Scholar
[4] Bryce, R.A., “On certain varieties of metabelian groups”, Ph.D. Thesis, Austral. Nat. Univ., 1967.Google Scholar
[5] Bryce, R.A., “Metabelian groups and varieties”, submitted to Philos. Trans. Roy. Soc.Google Scholar
[6] Kovács, L.G. and Newman, M.F., “Varieties of metabelian groups”, (in preparation).Google Scholar
[7] Kovács, L.G. and Newman, M.F., “On non-Cross varieties of groups”, (in preparation).Google Scholar
[8] Neumann, Hanna, Varieties of Groups. (Ergebnisse der Mathematik, und ihrer Grenzgebiete, Band 37, Springer-Verlag, Berlin, 1967).CrossRefGoogle Scholar
[9] Schenkman, Eugene, “The splitting of certain solvable groups”, Proc. Amer. Math. Soc. 6 (1955), 286–290.CrossRefGoogle Scholar
[10] Weichsel, Paul M., “On metabelian p-groups”, J. Austral. Math. Soc. 1 (1967), 55–63.Google Scholar