The existence and construction of a family of block-transitive 2-(v, 6, 1) designs

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:116

Article

Ding Shifeng

关键词: Design;    Block-transitive;    Weil's theorem;   

DOI  :  10.1016/j.jcta.2008.05.003

来源: Elsevier

【 摘 要 】

Let G be a block-transitive automorphism group of a 2-(v, k, 1) design E). It has been shown that the pairs (G. D) fall into three classes: those where G is unsolvable and is flag-transitive, those where G is a subgroup of A Gamma L(1, q). and those where G is solvable and is of small order. Not much is known about the latter two classes. In this paper, we investigate the existence of 2-(v, 6, 1) designs admitting a block-transitive automorphism group G < AGL(1, q). Using Weil's theorem oil character sums, the following theorem is proved: if a prime power q is large enough and q 31 (mod 60) then there is a 2-(v, 6, 1) design which has a block-transitive, but nonflag-transitive automorphism group G. Moreover, using computers, some concrete examples are given when q is small. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free