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arXiv · 1707.05105

Classification of finite groups that admit an oriented regular representation

Joy Morris·Pablo Spiga
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Abstract

This is the third, and last, of a series of papers dealing with oriented regular representations. Here we complete the classification of finite groups that admit an oriented regular representation (or ORR for short), and give a complete answer to a 1980 question of Laszlo Babai: "Which [finite] groups admit an oriented graph as a DRR?" It is easy to see and well-understood that generalised dihedral groups do not admit ORRs. We prove that, with 11 small exceptions (having orders ranging from 8 to 64), every finite group that is not generalised dihedral has an ORR.

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Joy Morris, Pablo Spiga. 2017-07-17. Classification of finite groups that admit an oriented regular representation. https://doi.org/10.1112/blms.12177

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