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On soluble just-non-Cross varieties of groups

Published online by Cambridge University Press:  17 April 2009

J. M. Brady
J. M. Brady
Affiliation:
Australian National University, Canberra, ACT.
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Abstract

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We prove a partial confirmation of Kovács and Newman's conjecture that a just-non-Cross variety is soluble if and only if it is in the following list: , , , , where p, q and r are any three distinct primes.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 3 , December 1970 , pp. 313 - 323
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Brady, J.M., On the classification of just-non-Cross varieties of groups”, Bull. Austral. Math. Soc. 3 (1970), 293–311.CrossRefGoogle Scholar
[2]Brady, J.M., Bryce, R.A. and Cossey, John, “On certain abelian-by-nilpotent varieties”, Bull. Austral. Math. Soc. 1 (1969), 403–416.CrossRefGoogle Scholar
[3]Cossey, P.J., “On varieties of 4-groups”, Ph.D. thesis, Australian National University, 1966. See also Proc. Internat. Conf. Theory of Groups, Austral. Nat. Univ., Canberra, 1965, 71 (Gordon and Breach, New York, 1967).Google Scholar
[4]Huppert, Bertram, Endliahe Gruppen I (Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
[5]Kovács, L.G. and Newman, M.F., “Cross varieties of groups”, Proc. Roy. Soc. Ser. A. 292 (1966), 530–536.Google Scholar
[6]Kovács, L.G. and Newman, M.F., “Just-non-Cross varieties”, Proc. Internat. Conf. Theory of Groups, Austral. Nat. Univ., Canberra, 1965, 221–223 (Gordon and Breach, New York, 1967).Google Scholar
[7]Kovács, L.G. and Newman, M.F., “On non-Cross varieties of groups”, J. Austral. Math. Soc. (to appear).Google Scholar
[8]Neumann, Hanna, Varieties of groups (Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 37, Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar