Realization of Groups with Pairing as Jacobians of Finite Graphs

@inproceedings{GAUDET2014RealizationOG,
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},
year={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