On the Non-existence of Semiregular Relative Difference Sets in Groups with All Sylow Subgroups Cyclic | Designs, Codes and Cryptography
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On the Non-existence of Semiregular Relative Difference Sets in Groups with All Sylow Subgroups Cyclic

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Abstract

We show that a group with all Sylow subgroups cyclic (other than \(\mathbb{Z}_4\)) cannot contain a normal semiregular relative difference set (RDSs). We also give a new proof that dihedral groups cannot contain (normal) semiregular RDSs either.

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Authors and Affiliations

  1. Department of Mathematics, RMIT University, GPO Box 2476V, Melbourne, VIC 3001, Australia

    John C. Galati

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  1. John C. Galati
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Correspondence to John C. Galati.

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Galati, J.C. On the Non-existence of Semiregular Relative Difference Sets in Groups with All Sylow Subgroups Cyclic. Des Codes Crypt 36, 29–31 (2005). https://doi.org/10.1007/s10623-003-1159-1

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  • DOI: https://doi.org/10.1007/s10623-003-1159-1

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