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Communications in Algebra Volume 40, 2012 - Issue 12
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Original Articles

Lie Properties of Symmetric Elements Under Oriented Involutions

John H. Castillo Gómez Departamento de Matemáticas y Estadística, Universidad de Nariño, San Juan de Pasto, Nariño, ColombiaCorrespondence[email protected]
&
César Polcino Milies Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brasil
Pages 4404-4419 | Received 21 Jun 2011, Published online: 10 Oct 2012
 
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Abstract

We study the Lie nilpotency and Lie n-Engel properties of symmetric elements under oriented involutions. In some cases, the results obtained are similar to the ones in the case of the classical involution, but interesting new situations arise.

2010 Mathematics Subject Classification:

ACKNOWLEDGMENTS

The results of this article are part of Castillo's Ph.D. thesis, at the Instituto de Matemática e Estatística of the Universidade de So Paulo, under the guidance of Prof. C. Polcino Milies. The authors are grateful to the referee for comments and suggestions that helped to improve the final version of this article. This work was partially supported by CAPES, CNPq. procs. 141857/2011-0, 300243/79-0(RN) and FAPESP proc. 09/52665-0 of Brazil.

Notes

Communicated by S. Sehgal.

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