Makarenko, N.Yu. and Khukhro, E. I.
(1998)
*Lie rings admitting an automorphism of order 4 with few fixed points. II.*
Algebra and Logic, 37
(2).
pp. 78-91.
ISSN 0002-5232

Full content URL: http://dx.doi.org/10.1007/BF02671594

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Item Type: | Article |
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Item Status: | Live Archive |

## Abstract

We consider a Lie ring (algebra) L that admits an automorphism Ï� of order 4 with a finite number m of fixed points (with a fixed-point subalgebra of finite dimension m). It is proved that L contains a subring S of m-bounded index in the additive group L (a subalgebra S of m-bounded codimension), which possesses a nilpotent ideal I of class bounded by some constant, such that the factor-ring S/I is nilpotent of class â�¤ 2. As a consequence, it is proved that, under the same conditions, L has a subring G of m-bounded index in the additive group of L (a subalgebra G of m-bounded codimension), in which an ideal generated by the Lie subring G, Ï�2 = ã��-g+g Ï�2 |g â�� Gã�� (the subalgebra G, Ï�2 = ã��-g+gÏ�2 |g â�� Gã�� is an ideal in G which) is nilpotent of class bounded by some constant (and its factor-algebra G/G, Ï�2 is nilpotent of class â�¤ 2 with a derived algebra (square) of m-bounded dimension). In proofs, we use the results of 1 and develop further the version of the method of generalized centralizers employed therein. Â© 1998 Plenum Publishing Corporation.

Additional Information: | Supported by RFFR grant No. 94-01-00048 |
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Keywords: | Algebra, Logic |

Subjects: | G Mathematical and Computer Sciences > G100 Mathematics |

Divisions: | College of Science > School of Mathematics and Physics |

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ID Code: | 15621 |

Deposited On: | 19 Nov 2014 14:39 |

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