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The Group of the Quadratic Residue Tournament

Published online by Cambridge University Press:  20 November 2018

Myron Goldberg
Myron Goldberg*
Affiliation:
University of Alberta, Edmonton, Alberta
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A tournament Tn is a set of n nodes a 1a 2, …, an such that every pair (ai , aj ) of distinct nodes is joined by exactly one of the oriented edges or . If is in Tn , then we say that ai dominates aj and write ai → aj .

The (automorphism) group G(Tn ) of a tournament Tn is the group of all permutations ϕ of the nodes of Tn such that ϕ(a)→ϕ(b) if and only if a → b. It is known [9] that there exist tournaments whose group is abstractly isomorphic to a given group H if and only if H has odd order; thus all tournament groups are solvable, by the Feit-Thompson Theorem [7].

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 1 , March 1970 , pp. 51 - 54
Copyright
Copyright © Canadian Mathematical Society 1970

References

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