This article is cited in 2 papers

RESEARCH ARTICLE

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

Vitaly I. Sushchansky, Nataliya V. Netreba

Silesian University of Technology, Gliwice, Poland and Kyiv Taras Shevchenko University, Kyiv, Ukraine

Abstract: We define a wreath product of a Lie algebra $L$ with the one-dimensional Lie algebra $L_1$ over $\mathbb F_p$ and determine some properties of this wreath product. We prove that the Lie algebra associated with the Sylow p-subgroup of finite symmetric group $S_{p^m}$ is isomorphic to the wreath product of $m$ copies of $L_1$. 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.

Keywords: Lie algebra, wreath product, semidirect product, Lie algebra associated with the lower central series of the group, Sylow p-subgroup, symmetric group.

MSC: 17B30, 17B60, 20F18, 20F40

Received: 27.03.2005
Revised: 05.04.2005

Language: English

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