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Abelian groups

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Full-Text Articles in Discrete Mathematics and Combinatorics

Hamilton Decompositions Of Certain 6-Regular Cayley Graphs On Abelian Groups With A Cyclic Subgroup Of Index Two, Erik E. Westlund Nov 2012

Hamilton Decompositions Of Certain 6-Regular Cayley Graphs On Abelian Groups With A Cyclic Subgroup Of Index Two, Erik E. Westlund

Faculty and Research Publications

Alspach conjectured that every connected Cayley graph of even valency on a finite Abelian group is Hamilton-decomposable. Using some techniques of Liu, this article shows that if A is an Abelian group of even order with a generating set {a,b}, and A contains a subgroup of index two, generated by c, then the 6-regular Cayley graph is Hamilton-decomposable.

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New Constructions Of Menon Difference Sets, K. T. Arasu, James A. Davis, Jonathan Jedwab, Surinder K. Sehgal Nov 1993

New Constructions Of Menon Difference Sets, K. T. Arasu, James A. Davis, Jonathan Jedwab, Surinder K. Sehgal

Department of Math & Statistics Faculty Publications

Menon difference sets have parameters (4N2, 2N2 − N, N2 − N). These have been constructed for N = 2a3b, 0 ⩽ a,b, but the only known constructions in abelian groups require that the Sylow 3-subgroup be elementary abelian (there are some nonabelian examples). This paper provides a construction of difference sets in higher exponent groups, and this provides new examples of perfect binary arrays.

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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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