Application of Gaschutz Theorem to relative difference sets in non-abelian groups

Galati, J 2003, 'Application of Gaschutz Theorem to relative difference sets in non-abelian groups', Journal of Combinatorial Designs, vol. 11, no. 5, pp. 307-311.


Document type: Journal Article
Collection: Journal Articles

Title Application of Gaschutz Theorem to relative difference sets in non-abelian groups
Author(s) Galati, J
Year 2003
Journal name Journal of Combinatorial Designs
Volume number 11
Issue number 5
Start page 307
End page 311
Total pages 4
Publisher John Wiley and Sons
Abstract Let G be a finite group other than 4 and suppose that G contains a semiregular relative difference set (RDS) relative to a central subgroup U. We apply Gaschütz' Theorem from finite group theory to show that if G/U has cyclic Sylow subgroups for each prime divisor of |U|, then G splits over U. A corollary of this result is that a finite group (other than 4) in which all Sylow subgroups are cyclic cannot contain a central semiregular RDS. We also include an example, originally discovered by D.L. Flannery, which shows that our main theorem is not true in general when U is a (not necessarily central) abelian normal subgroup of G.
Subject Algebra and Number Theory
DOI - identifier 10.1002/jcd.10041
Copyright notice © 2003 Wiley Periodicals
ISSN 1063-8539
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