An effective version of the Lazard correspondence

作者：Cicalo Serena; de Graaf Willem A^*; Vaughan Lee Michael

来源：Journal of Algebra, 2012, 352(1): 430-450.

DOI：10.1016/j.jalgebra.2011.11.031

• p-Groups
• Lie rings
• Lazard correspondence
• Effective methods

The Lazard correspondence establishes an equivalence of categories between p-groups of nilpotency class less than p and nilpotent Lie rings of the same class and order. The main tools used to achieve this are the Baker-Campbell-Hausdorff formula and its inverse formulae. Here we describe methods to compute the inverse Baker-Campbell-Hausdorff formulae. Using these we get an algorithm to compute the Lie ring structure of a p-group of class %26lt; p. Furthermore, the Baker-Campbell-Hausdorff formula yields an algorithm to construct a p-group from a nilpotent Lie ring of order p(n) and class less than p. At the end of the paper we discuss some applications of, and practical experiences with, the algorithms.

• 出版日期2012-2-15