On non-Abelian group difference sets
type: Item
instance of: scholarly article
title: On non-Abelian group difference sets
zbMATH Open document ID: 0778.05024
DOI: 10.1016/0012-365X(93)90226-J
author: Shuhong Gao
author: Wandi Wei
published in: Discrete Mathematics
publication date: 1993-08-30T00:00:00Z
review text: Let \(D\) be a symmetric \((v,k,\lambda)\)-design which admits an automorphism group \(\Gamma\) that acts sharply transitively on the points and lines of \(D\). Designs with this property can be described using difference sets. The normalizer \(N\) of \(\Gamma\) in the full automorphism group of a design is the group generated by \(\Gamma\) and the multiplier group of the difference set. The main theorem describes a construction of subgroups \(\Delta\) of \(N\) (different from \(\Gamma)\) which again act regularly on points and lines. The paper contains many examples and applications of the main theorem. An extended abstract of the paper has been published in [J. Sichuan Univ., Nat. Sci. Ed. 26, Spec. Issue, 136- 139 (1989; Zbl 0748.05027)].
reviewed by: Alexander Pott
Mathematics Subject Classification ID: 05B10
zbMATH DE Number: 179591
zbMATH Keywords: automorphism group
zbMATH Keywords: difference sets
zbMATH Keywords: design
MaRDI profile type: Publication
cites work: Cyclic difference sets
cites work: Q3686719
cites work: Difference Sets in a Finite Group
cites work: Q3715120
cites work: A summary of noncylic difference sets, \(k<20\)
cites work: Q4346801
full work available at URL: 0012-365x(93)90226-j
OpenAlex ID: W2069343998
description: scientific article; zbMATH DE number 179591