Enumeration of 2-(21, 6, 3) designs with automorphisms of order 7 or 5
type: Item
instance of: scholarly article
zbMATH Open document ID: 0962.05013
author: Stoyan Kapralov
author: Svetlana Topalova
publication date: 2001-05-30T00:00:00Z
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 1600919
zbMATH Keywords: design
zbMATH Keywords: automorphism
MaRDI profile type: Publication
title: Enumeration of 2-(21, 6, 3) designs with automorphisms of order 7 or 5
published in: Ars Combinatoria
review text: The authors describe all \(2\)-\((21,6,3)\) designs (each pair in three blocks) which admit an automorphism \(\varphi \) of order \(p\), \(p \geq 5\) a prime. General considerations imply that \(p \leq 7\) and that \(\varphi \) fixes no block or point if \(p =7\). It is proved that if \(p=5\), then \(\varphi \) fixes one point, two blocks and every non-fixed point is contained in at most one fixed block. This information (together with a certain rough classification criterion) is then used for a computer based search. It turns out that the order of the automorphism group of a design can be \(5\), \(10\), \(7\), \(14\), \(21\) or \(63\).
reviewed by: Aleš Drápal
description: scientific article; zbMATH DE number 1600919