Abstract
AbstractLet G be a finite group other than ℤ4 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 ℤ4) 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. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 307–311, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10041
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