On the Possible Automorphism Groups of a Steiner Quintuple System of Order 21


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Kolotoglu E. , Magliveras S. S.

JOURNAL OF COMBINATORIAL DESIGNS, vol.22, pp.495-505, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22
  • Publication Date: 2014
  • Doi Number: 10.1002/jcd.21370
  • Title of Journal : JOURNAL OF COMBINATORIAL DESIGNS
  • Page Numbers: pp.495-505

Abstract

A Steiner system S(4, 5, v) is called a Steiner quintuple systems of order v. The smallest order for which the existence, or otherwise, of a Steiner quintuple system is unknown is 21. In this article, we prove that, if an S(4, 5, 21) exists, the order of its full automorphism group is 1, 2, 3, 4, 5, 6, 7, or 10. (C) 2013 Wiley Periodicals, Inc.