Designs, Codes and Cryptography

, Volume 47, Issue 1–3, pp 243–247 | Cite as

On the Phan system of the Schur cover of SU(4, 32)

Article

Abstract

This article is part of the program described in Bennett et al. (in: Ivanov et al. (ed.) Groups, combinatorics, and geometry, 2003) [3]. We study the Phan amalgams and their universal completions that occur for q = 3 in rank n = 3 for the diagram A3 = D3, corresponding to SU(4, 32) ≅ Spin(6, 3). We show that the associated geometries admit universal 9-fold coverings, by showing that the universal completion of the Phan amalgam is the central extension of SU(4, 32) by its Schur multiplier. This information provides the last missing piece of information in the full classification of Phan amalgams and their universal completions for An and Dn.

Keywords

Phan theory Phan amalgam Group amalgams Incidence geometry Computer algebra GAP Coset enumeration ACE 

AMS Classifications

20G40 20E42 51E24 57M07 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.FB Mathematik, TU DarmstadtDarmstadtGermany

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