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On varieties of soluble groups II

Published online by Cambridge University Press:  17 April 2009

J.R.J. Groves
J.R.J. Groves
Affiliation:
University of Manitoba, Winnipeg, Canada.
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Abstract

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It is shown that, in a variety which does not contain all metabelian groups and is contained in a product of (finitely many) varieties each of which is soluble or locally finite, every group is an extension of a group of finite exponent by a nilpotent group by a group of finite exponent.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 7 , Issue 3 , December 1972 , pp. 437 - 441
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Bryce, R.A., “Metabelian groups and varieties”, Philos. Trans. Roy. Soc. London Ser. A 266 (1970), 281–355.Google Scholar
[2]Groves, J.R.J., “On varieties of soluble groups”, Bull. Austral. Math. Soc. 5 (1971), 95–109.Google Scholar
[3]Groves, J.R.J., “Varieties of soluble groups and a dichotomy of P. Hall”, Bull. Austral. Math. Soc. 5 (1971), 391–410.Google Scholar
[4]Gupta, Narain, “On metanilpotent varieties of groups”, Canad. J. Math. 22 (1970), 875–877.CrossRefGoogle Scholar
[5]Hall, P., “Finiteness conditions for soluble groups”, Proc. London Math. Soc. (3) 4 (1954), 419–436.Google Scholar
[6]Каргаполов, М.И.Цуркин, В.А.[Kargapolov, M.I., Čurkin, V.A., “О миогообразиях разрешимых групп” [On varieties of soluble groups], Algebra i Logika 10 (1971), 651–657.Google Scholar
[7]Neumann, Hanna, Varieties of groups (Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 37. Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
[8]Šmel'kin, A.L., “On soluble groups varieties”, Soviet Math. Dokl. 9 (1968), 100–103.Google Scholar
[9]Wehrfritz, B.A.F., “Groups of automorphisms of soluble groups”, Proc. London Math. Soc. (3) 20 (1970), 101–122.CrossRefGoogle Scholar