Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups

Abstract

We define a wreath product of a Lie algebra L with the one-dimensional Lie algebra L1 over Fp and determine some properties of this wreath product. We prove that the Lie algebra associated with the Sylow p-subgroup of finite symmetric group Spm is isomorphic to the wreath product of m copies of L1. As a corollary we describe the Lie algebra associated with Sylow p-subgroup of any symmetric group in terms of wreath product of one-dimensional Lie algebras.