Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 311-330 |
| Number of pages | 20 |
| Journal | Journal of Algebra |
| Volume | 421 |
| DOIs | |
| Publication status | Published - 2015 |
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AS-configurations and skew-translation generalised quadrangles. / Bamberg, John; Glasby, Stephen; Swartz, Eric.
In: Journal of Algebra, Vol. 421, 2015, p. 311-330.Research output: Contribution to journal › Article
TY - JOUR
T1 - AS-configurations and skew-translation generalised quadrangles
AU - Bamberg, John
AU - Glasby, Stephen
AU - Swartz, Eric
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 -