Realization of Groups with Pairing as Jacobians of Finite Graphs

  title={Realization of Groups with Pairing as Jacobians of Finite Graphs},
  author={LOUIS GAUDET and David Jensen and Dhruv Ranganathan and NICHOLAS WAWRYKOW and THEODORE WEISMAN and A BSTRACT},
  • LOUIS GAUDET, David Jensen, +3 authors A BSTRACT
  • Published 2014
We study which groups with pairing can occur as the Jacobian of a finite graph. We provide explicit constructions of graphs whose Jacobian realizes a large fraction of odd groups with a given pairing. Conditional on the generalized Riemann hypothesis, these constructions yield all groups with pairing of odd order, whose prime factors are sufficiently large. For groups with pairing of even order, we provide a partial answer to this question, for a certain restricted class of pairings. Finally… CONTINUE READING


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Publications referenced by this paper.
Showing 1-10 of 15 references

Multiplicative number theory, volume 74 of Graduate Texts in Mathematics

  • Harold Davenport
  • 2000
Highly Influential
1 Excerpt

Prime splitting in abelian number fields and linear combinations of dirichlet characters

  • Paul Pollack
  • International Journal of Number Theory,
  • 2014

The distribution of sandpile groups of random graphs

  • Melanie Matchett Wood
  • 2014
3 Excerpts

Lorenzini . Arithmetical graphs

  • J Dino
  • Physical Review Letters
  • 1990

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