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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Complements of intervals and prefrattini subalgebras of solvable Lie algebras


Author: David A. Towers
Journal: Proc. Amer. Math. Soc. 141 (2013), 1893-1901
MSC (2010): Primary 17B05, 17B30, 17B50
Published electronically: December 21, 2012
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study a Lie-theoretic analogue of a generalisation of the prefrattini subgroups introduced by W. Gaschütz. The approach follows that of P. Hauck and H. Kurzweil for groups by first considering complements in subalgebra intervals. Conjugacy of these subalgebras is established for a large class of solvable Lie algebras.


References [Enhancements On Off] (What's this?)

  • 1. D.W. BARNES AND H.M. GASTINEAU-HILLS, `On the theory of soluble Lie algebras', Math. Z. 106 (1968), 343-354. MR 0232807 (38:1130)
  • 2. D.W. BARNES AND M.L. NEWELL, `Some theorems on saturated homomorphs of soluble Lie algebras', Math. Z. 115 (1970), 179-187. MR 0266969 (42:1871)
  • 3. P. HAUCK AND H. KURZWEIL, `A lattice-theoretic characterization of prefrattini subgroups', Manuscripta Math. 66 (1990), 295-301. MR 1031198 (91f:20026)
  • 4. D.A. TOWERS, `On complemented Lie algebras', J. London Math. Soc. (2) 22 (1980), 63-65. MR 579809 (81h:17006)
  • 5. D. A. TOWERS, `Solvable complemented Lie algebras', Proc. Amer. Math. Soc. 140 (2012), no. 11, 3823-3830. MR 2944723

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Additional Information

David A. Towers
Affiliation: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, England
Email: d.towers@lancaster.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11521-7
PII: S 0002-9939(2012)11521-7
Keywords: Lie algebras, complemented, solvable, Frattini ideal, prefrattini subalgebra, residual
Received by editor(s): September 9, 2011
Received by editor(s) in revised form: September 21, 2011
Published electronically: December 21, 2012
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.