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On the Possible Automorphism Groups of a Steiner Quintuple System of Order 21
Author(s) -
Kolotoğlu Emre,
Magliveras Spyros S.
Publication year - 2014
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21370
Subject(s) - steiner system , mathematics , combinatorics , order (exchange) , automorphism , automorphism group , steiner tree problem , group (periodic table) , discrete mathematics , chemistry , organic chemistry , finance , economics
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.