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Siberian Mathematical Journal

, Volume 42, Issue 5, pp 996–1000 | Cite as

On Solvability of Lie Rings with an Automorphism of Finite Order

  • E. I. Khukhro
Article

Abstract

A new criterion for a Lie ring with a semisimple automorphism of finite order to be solvable is proved. It generalizes the effective version of Winter's criterion obtained earlier by Khukhro and Shumyatsky and by Bergen and Grzeszczuk in replacing the ideal generated by a certain set by the subring generated by this set. The proof is inspired by the original theorem of Kreknin on solvability of Lie rings with regular automorphisms of finite order and is conducted mostly in terms of Lie rings graded by a finite cyclic group.

Keywords

Cyclic Group Finite Order Effective Version Original Theorem Regular Automorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Khukhro E. I. and Shumyatskiî P. V., “Fixed points of automorphisms of Lie rings and locally finite groups,” Algebra and Logic, 34, No. 6, 395-405 (1995).Google Scholar
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    Bergen J. and Grzeszczuk P., “Gradings, derivations, and automorphisms of nearly associative algebras,” J. Algebra, 179, 732-750 (1996).Google Scholar
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    Khukhro E. I. and Makarenko N. Yu., “Lie rings admitting an automorphism of order 4 with few fixed points,” Algebra and Logic, 35, No. 1, 21-43 (1996).Google Scholar
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    Khukhro E. I. and Makarenko N. Yu., “Lie rings admitting an automorphism of order 4 with few fixed points. II,” Algebra and Logic, 37, No. 2, 78-91 (1998).Google Scholar

Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • E. I. Khukhro
    • 1
  1. 1.The Sobolev Institute of MathematicsNovosibirsk

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