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Inaccessible varieties of groups

Published online by Cambridge University Press:  09 April 2009

L. G. Kovács
L. G. Kovács
Affiliation:
Australian National University, Canberra
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A weak but still unsolved version of the first half of Problem 7 in Hanna Neumann's book [5] asks whether the product of a nontrivial join-irreducible variety and an arbitrary variety is necessarily also join-irreducible. One of the results of this paper is a positive answer provided either is abelian or the infiniterank free groups of have no nontrivial abelian verbal subgroups. For a general discussion, see [4]; all unexplained notation is as in [5].

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 4 , June 1974 , pp. 506 - 510
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Brady, J. M., ‘On the classification of just-non-Cross varieties of groups’, Bull. Austral. Math. Soc. 3 (1970), 293–311.Google Scholar
[2]Brady, J. M., ‘On soluble just-non-Cross varieties of groups’, Bull. Austral. Math. Soc. 3 (1970), 313–323.CrossRefGoogle Scholar
[3]Dunwoody, M. J., ‘On product varieties’, Math. Z. 104 (1968), 91–97.Google Scholar
[4]Kovács, L. G. and Newman, M. F., ‘Hanna Neumann's problems’, to appear in Proc. Second Internat. Conf. Theory of Groups, Austral. Nat. Univ. Canberra, 1973; Lecture Notes in Mathematics 372, Springer-Verlag, Berlin, Heidelberg, New York, 1974.Google Scholar
[5]Neumann, Hanna, Varieties of groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 37, Springer-Verlag, Berlin, Heidelberg, New York, 1967.Google Scholar