The Orders of Nonsingular Derivations of Lie Algebras of Characteristic Two
نویسنده
چکیده
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 Np 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. In this paper we continue this study in the case of characteristic two. Among other results, we prove that any divisor n of 2 − 1 with n > (2 − n) belongs to N2. Our methods consist of elementary arguments with polynomials over finite fields and a little character theory of finite groups.
منابع مشابه
Many Numbers Can Be Orders of Nonsingular Derivations of Modular Lie Algebras
Abstract. A study of the set Np 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 show the abundance of elements of Np. Our main result shows that any divisor n of q − 1, where q is a power of p, such that n ≥...
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تاریخ انتشار 2006