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University of Richmond

Mathematics

Relative difference set

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A New Family Of Relative Difference Sets In 2-Groups, James A. Davis, Jonathan Jedwab Sep 1999

A New Family Of Relative Difference Sets In 2-Groups, James A. Davis, Jonathan Jedwab

Department of Math & Statistics Faculty Publications

We recursively construct a new family of (26d+4, 8, 26d+4, 26d+1) semi-regular relative difference sets in abelian groups G relative to an elementary abelian subgroup U. The initial case d = 0 of the recursion comprises examples of (16, 8, 16, 2) relative difference sets for four distinct pairs (G, U).

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New Families Of Semi-Regular Relative Difference Sets, James A. Davis, Jonathan Jedwab, Miranda Mowbray Feb 1998

New Families Of Semi-Regular Relative Difference Sets, James A. Davis, Jonathan Jedwab, Miranda Mowbray

Department of Math & Statistics Faculty Publications

We give two constructions for semi-regular relative difference sets (RDSs) in groups whose order is not a prime power, where the order u of the forbidden subgroup is greater than 2. No such RDSs were previously known. We use examples from the first construction to produce semi-regular RDSs in groups whose order can contain more than two distinct prime factors. For u greater than 2 these are the first such RDSs, and for u = 2 we obtain new examples.

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Construction Of Relative Difference Sets In P-Groups, James A. Davis May 1992

Construction Of Relative Difference Sets In P-Groups, James A. Davis

Department of Math & Statistics Faculty Publications

Jungnickel (1982) and Elliot and Butson (1966) have shown that (pj+1,p,pj+1,pj) relative difference sets exist in the elementary abelian p-group case (p an odd prime) and many 2-groups for the case p = 2. This paper provides two new constructions of relative difference sets with these parameters; the first handles any p-group (including non-abelian) with a special subgroup if j is odd, and any 2-group with that subgroup if j is even. The second construction shows that if j is odd, every abelian group …

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An Exponent Bound For Relative Difference Sets In P-Groups, James A. Davis Jan 1992

An Exponent Bound For Relative Difference Sets In P-Groups, James A. Davis

Department of Math & Statistics Faculty Publications

An exponent bound is presented for abelian (pi+j, pi, pi+j, pi) relative difference sets: this bound can be met for i≤j.

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