Point regular groups of automorphisms of generalised quadrangles

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:118

Article

Bamberg, John¹  Giudici, Michael¹ 

[1] Univ Western Australia, Sch Math & Stat, Ctr Math Symmetry & Computat, Crawley, WA 6009, Australia

关键词: Generalised quadrangle;    Regular action;    p-Group;   

DOI  :  10.1016/j.jcta.2010.11.004

来源: Elsevier

【 摘 要 】

We study the point regular groups of automorphisms of some of the known generalised quadrangles. In particular we determine all point regular groups of automorphisms of the thick classical generalised quadrangles. We also construct point regular groups of automorphisms of the generalised quadrangle of order (q - 1, q + 1) obtained by Payne derivation from the classical symplectic quadrangle W(3, q). For q = p(f) with f >= 2 we obtain at least two nonisomorphic groups when p >= 5 and at least three nonisomorphic groups when p = 2 or 3. Our groups include nonabelian 2-groups, groups of exponent 9 and nonspecial p-groups. We also enumerate all point regular groups of automorphisms of some small generalised quadrangles. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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