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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    BARNES, DONALD W. 2015. CONDITIONS FOR A SCHUNCK CLASS TO BE A FORMATION. Bulletin of the Australian Mathematical Society, Vol. 91, Issue. 01, p. 69.


    BARNES, DONALD W. 2014. CHARACTER CLUSTERS FOR LIE ALGEBRA MODULES OVER A FIELD OF NONZERO CHARACTERISTIC. Bulletin of the Australian Mathematical Society, Vol. 89, Issue. 02, p. 234.


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  • Bulletin of the Australian Mathematical Society, Volume 86, Issue 2
  • October 2012, pp. 322-326

ON LOCALLY DEFINED FORMATIONS OF SOLUBLE LIE AND LEIBNIZ ALGEBRAS

  • DONALD W. BARNES (a1)
  • DOI: http://dx.doi.org/10.1017/S0004972711003443
  • Published online: 02 February 2012
Abstract
Abstract

It is well known that all saturated formations of finite soluble groups are locally defined and, except for the trivial formation, have many different local definitions. I show that for Lie and Leibniz algebras over a field of characteristic 0, the formations of all nilpotent algebras and of all soluble algebras are the only locally defined formations and the latter has many local definitions. Over a field of nonzero characteristic, a saturated formation of soluble Lie algebras has at most one local definition, but a locally defined saturated formation of soluble Leibniz algebras other than that of nilpotent algebras has more than one local definition.

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[1]D. W. Barnes , ‘Saturated formations of soluble Lie algebras in characteristic 0’, Arch. Math. (Basel) 30 (1978), 477480.

[3]D. W. Barnes and H. M. Gastineau-Hills , ‘On the theory of soluble Lie algebras’, Math. Z. 106 (1968), 343354.

[4]K. Doerk and T. Hawkes , Finite Soluble Groups (De Gruyter, Berlin–New York, 1992).

[5]J.-L. Loday and T. Pirashvili , ‘Leibniz representations of Lie algebras’, J. Algebra 181 (1996), 414425.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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