AS-configurations and skew-translation generalised quadrangles

John Bamberg; S. P. Glasby; Eric Swartz

AS-configurations and skew-translation generalised quadrangles

Group Theory 2014-07-22 v2

Authors: John Bamberg , S. P. Glasby , Eric Swartz

Abstract

The only known skew-translation generalised quadrangles (STGQ) having order $(q,q)$ , with $q$ even, are translation generalised quadrangles. Equivalently, the only known groups $G$ of order $q^3$ , $q$ even, admitting an Ahrens-Szekeres (AS-)configuration are elementary abelian. In this paper we prove results in the theory of STGQ giving (i) new structural information for a group $G$ admitting an AS-configuration, (ii) a classification of the STGQ of order $(8,8)$ , and (iii) a classification of the STGQ of order $(q,q)$ for odd $q$ (using work of Ghinelli and Yoshiara).

Keywords

skew-translation generalised quadrangles AS-configurations Ahrens-Szekeres configuration elementary abelian groups classification structural information

Cite

@article{arxiv.1405.5063,
  title  = {AS-configurations and skew-translation generalised quadrangles},
  author = {John Bamberg and S. P. Glasby and Eric Swartz},
  journal= {arXiv preprint arXiv:1405.5063},
  year   = {2014}
}

Comments

A shorter version of this paper will appear in J. Algebra. This arXiv version includes our supporting GAP code in an Appendix. The structure of the proof was modified and Lemma 4.15 was inserted. Some other minor corrections were made

AS-configurations and skew-translation generalised quadrangles

Abstract

Keywords

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