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 László 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 ORR s. 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.
Morris, J., Spiga, P. (2018). Classification of finite groups that admit an oriented regular representation. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 50(5), 811-831 [10.1112/blms.12177].
Classification of finite groups that admit an oriented regular representation
Spiga P.
2018
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 László 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 ORR s. 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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