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 -Rfnet-temp p 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 2 k - 1 with n 4 > (2k - n)3 belongs to N2. Our methods consist of elementary arguments with polynomials over finite fields and a little character theory of finite groups.
Mattarei, S. (2007). The orders of nonsingular derivations of Lie algebras of characteristic two. ISRAEL JOURNAL OF MATHEMATICS, 160(1), 23-40 [10.1007/s11856-007-0054-2].
The orders of nonsingular derivations of Lie algebras of characteristic two
Mattarei, S
2007
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 -Rfnet-temp p 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 2 k - 1 with n 4 > (2k - n)3 belongs to N2. Our methods consist of elementary arguments with polynomials over finite fields and a little character theory of finite groups.File | Dimensione | Formato | |
---|---|---|---|
Mattarei-2007-Isr J Math-VoR.pdf
Solo gestori archivio
Descrizione: Article
Tipologia di allegato:
Publisher’s Version (Version of Record, VoR)
Licenza:
Tutti i diritti riservati
Dimensione
218.21 kB
Formato
Adobe PDF
|
218.21 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.