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 < 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. © 2011 Elsevier Inc. All rights reserved.

An effective version of the Lazard correspondence / S., Cicalò; De Graaf, Willem Adriaan; M., Vaughan Lee. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 2012, 352:(2012), pp. 430-450. [10.1016/j.jalgebra.2011.11.031]

An effective version of the Lazard correspondence

De Graaf, Willem Adriaan;
2012-01-01

Abstract

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 < 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. © 2011 Elsevier Inc. All rights reserved.
2012
S., Cicalò; De Graaf, Willem Adriaan; M., Vaughan Lee
An effective version of the Lazard correspondence / S., Cicalò; De Graaf, Willem Adriaan; M., Vaughan Lee. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 2012, 352:(2012), pp. 430-450. [10.1016/j.jalgebra.2011.11.031]
File in questo prodotto:
File Dimensione Formato  
lazard.pdf

accesso aperto

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 254.46 kB
Formato Adobe PDF
254.46 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/90453
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 11
social impact