TY - JOUR
T1 - AS-configurations and skew-translation generalised quadrangles
AU - Bamberg, John
AU - Glasby, Stephen
AU - Swartz, Eric
N1 - Funding Information:
We would like to thank Professors Ghinelli and Ott for their help with the proof of Lemma A.1 . We also thank Dr Gabriel Verret for his comments on an earlier draft. The first author acknowledges the support of the Australian Research Council Future Fellowship FT120100036 . The second author acknowledges the support of the Australian Research Council Discovery Grants DP130100106 and DP1401000416 . The third author acknowledges the support of the Australian Research Council Discovery Grant DP120101336 .
Publisher Copyright:
© 2014 .
PY - 2015
Y1 - 2015
N2 - 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 q3, 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).
AB - 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 q3, 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).
KW - Generalised quadrangle
KW - P-Group
KW - Partial difference set
KW - Skew-translation
UR - http://www.scopus.com/inward/record.url?scp=84908576843&partnerID=8YFLogxK
UR - http://www.mendeley.com/research/asconfigurations-skewtranslation-generalised-quadrangles
U2 - 10.1016/j.jalgebra.2014.08.031
DO - 10.1016/j.jalgebra.2014.08.031
M3 - Article
VL - 421
SP - 311
EP - 330
JO - Journal of Algebra
JF - Journal of Algebra
SN - 0021-8693
ER -