The orders of nonsingular derivations of Lie algebras of characteristic two |
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Authors: | S Mattarei |
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Institution: | (1) Dipartimento di Matematica, Università degli Studi di Trento, via Sommarive 14, I-38050 Povo (Trento), Italy |
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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
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 n
4 > (2k − n)3 belongs to
. 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”. |
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Keywords: | |
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