Mattarei, Sandro
(2009)
*A sufficient condition for a number to be the order of a nonsingular derivation of a Lie algebra.*
Israel Journal of Mathematics, 171
(1).
pp. 1-14.
ISSN 0021-2172

Full content URL: http://dx.doi.org/10.1007/s11856-009-0036-7

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

## Abstract

A study of the set N_p of positive integers which occur as orders of nonsingular derivations of finite-dimensional non-nilpotent Lie algebras of characteristic p>0 was initiated by Shalev and continued by the present author. The main goal of this paper is to produce more elements of N_p. Our main result shows that any divisor n of q − 1, where q is a power of p, such that n ≥ (p − 1)^{1/p} (q − 1)^{1−1/(2p)}, necessarily belongs to N_p. This extends its special case for p = 2 which was proved in a previous paper by a different method.

Keywords: | Lie algebra, injective derivation |
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Subjects: | G Mathematical and Computer Sciences > G110 Pure Mathematics |

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

ID Code: | 18504 |

Deposited On: | 11 Dec 2015 09:09 |

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