Lie Properties of Symmetric Elements Under Oriented Involutions

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.

Key Words:

• Involution
• Lie n-Engel
• Lie nilpotent
• Symmetric elements

2010 Mathematics Subject Classification:

• 16W10
• 16U80
• 20C07

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.