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