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Realization of Groups with Pairing as Jacobians of Finite Graphs

Author(s)
Gaudet, Louis; Jensen, David; Ranganathan, Dhruv; Wawrykow, Nicholas; Weisman, Theodore
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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Abstract
Abstract 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, and unconditionally, they yield all groups with pairing 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, we explore which finite abelian groups occur as the Jacobian of a simple graph. There exist infinite families of finite abelian groups that do not occur as the Jacobians of simple graphs.
Date issued
2018-11-02
URI
https://hdl.handle.net/1721.1/131386
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Springer International Publishing

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