The orders of nonsingular derivations of Lie algebras of characteristic two

Mattarei, S. (2007) The orders of nonsingular derivations of Lie algebras of characteristic two. Israel Journal of Mathematics, 160 (1). pp. 23-40. ISSN 0021-2172

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Abstract

Nonsingular derivations of modular Lie algebras which have finite multiplicative order play a role in the coclass theory for pro-p groups and Lie algebras. A study of the set NpNp of positive integers which occur as orders of nonsingular derivations of finite-dimensional nonnilpotent Lie algebras of characteristic p > 0 was initiated by Shalev and continued by the present author. In this paper we continue this study in the case of characteristic two. Among other results, we prove that any divisor n of 2k − 1 with n4 > (2k − n)3 belongs to N2N2 . Our methods consist of elementary arguments with polynomials over finite fields and a little character theory of finite groups.

This work was partially supported by Ministero dell’Istruzione e dell’Università, Italy, through PRIN “Graded Lie algebras and pro-p-groups of finite width”.

Keywords:Lie algebras
Subjects:G Mathematical and Computer Sciences > G100 Mathematics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:18507
Deposited On:16 Nov 2016 12:24

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