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5 results

  • Finitely presented centre-by-metabelian Lie algebras

  • R.M. Bryant, J.R.J. Groves
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 60 / Issue 2 / October 1999
    Published online by Cambridge University Press:
    17 April 2009, pp. 221-226
    Print publication:
    October 1999
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  • It is shown that finitely presented centre-by-metabelian Lie algebras are Abelian-by-finite-dimensional.

  • On varieties of soluble groups II

  • J.R.J. Groves
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 7 / Issue 3 / December 1972
    Published online by Cambridge University Press:
    17 April 2009, pp. 437-441
    Print publication:
    December 1972
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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.

  • Varieties of soluble groups

  • J.R.J. Groves
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 6 / Issue 1 / February 1972
    Published online by Cambridge University Press:
    17 April 2009, pp. 159-160
    Print publication:
    February 1972
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  • Varieties of soluble groups and a dichotomy of P. Hall

  • J.R.J. Groves
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 5 / Issue 3 / December 1971
    Published online by Cambridge University Press:
    17 April 2009, pp. 391-410
    Print publication:
    December 1971
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  • Let denote the variety of all abelian groups and, for each prime p, let p be the variety of all elementary abelian p-groups. Let be a subvariety of a product of (finitely many) varieties each of which is either soluble or Cross.

  • On varieties of soluble groups

  • J.R.J. Groves
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 5 / Issue 1 / August 1971
    Published online by Cambridge University Press:
    17 April 2009, pp. 95-109
    Print publication:
    August 1971
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  • We show that, under certain conditions, a soluble variety of groups which does not contain the variety of all metabelian groups is a finite exponent by nilpotent by finite exponent variety.