Abstract
A tournamentX is a TRR for a groupG if (a)G acts regularly on the vertices ofX and (b) Aut(X) is isomorphic toG. We correct some previous work of Babai and Imrich by showing thatZ 32 andZ 33 are the only groups of odd order without TRR's. Our methods are perhaps of independent interest, since we use a probabilistic approach.
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References
Babai, L. andImrich, W.,Tournament with given regular group. Aequationes Math.19 (1979), 232–244.
Godsil, C. D.,On the full automorphism group of a graph. Combinatorica1 (1981), 243–256.
Huppert, B.,Endliche Gruppen I. Springer, Berlin, 1979.
Imrich, W.,On graphical representations of groups. InInfinite and finite sets (Colloq. Keszthely, 1973), Vol. II, pp. 905–925. Colloq. Math. Soc. János Bolyai, Vol. 10, North-Holland, Amsterdam, 1975.
Suzuki, Michio,Group Theory I. Springer, Berlin, 1982.
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Godsil, C.D. Tournaments with prescribed regular automorphism group. Aeq. Math. 30, 55–64 (1986). https://doi.org/10.1007/BF02189910
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DOI: https://doi.org/10.1007/BF02189910