Nonabelian groups with \((96,20,4)\) difference sets
type: Item
instance of: scholarly article
title: Nonabelian groups with \((96,20,4)\) difference sets
zbMATH Open document ID: 1110.05015
author: Ken W. Smith
author: O. A. AbuGhneim
published in: The Electronic Journal of Combinatorics
publication date: 2007-03-12T00:00:00Z
full work available at URL: v14i1r8.html
review text: Summary: We resolve the existence problem of \((96,20,4)\) difference sets in 211 of 231 groups of order 96. If \(G\) is a group of order 96 with normal subgroups of orders 3 and 4 then by first computing 32- and 24-factor images of a hypothetical \((96,20,4)\) difference set in \(G\) we are able to either construct a difference set or show a difference set does not exist. Of the 231 groups of order 96, 90 groups admit \((96,20,4)\) difference sets and 121 do not. The ninety groups with difference sets provide many genuinely nonabelian difference sets. Seven of these groups have exponent 24. These difference sets provide at least 37 nonisomorphic symmetric \((96,20,4)\) designs.
Mathematics Subject Classification ID: 05B10
zbMATH DE Number: 5132842
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5132842