On locally defined formations of soluble Lie and Leibniz algebras

Authors

  • Donald William Barnes University of Sydney

Keywords:

Lie algebras, Leibniz algebras, saturated formations, local definition

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 non-zero 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. DOI: 10.1017/S0004972711003443

Author Biography

Donald William Barnes, University of Sydney

Honorary Associate School of Mathematics and Statistics

Published

2012-08-27

Issue

Vol. 86 No. 2 (2012)

Section

Articles
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