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Transitive Permutation Group

A transitive permutation group is a permutation group G acting on a set Omega with a single group orbit. Equivalently, for every alpha,beta in Omega, some g in G satisfies alpha^g=beta.

Thus transitivity is a property of a particular permutation action, not only of the abstract group. Transitive permutation groups are also called transitive groups.

See also

Group Orbit, Permutation Group, Transitive Group, Transitive Group Action

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References

Dixon, J. and Mortimer, B. Permutation Groups. New York: Springer-Verlag, 1996.

Cite this as:

Weisstein, Eric W. "Transitive Permutation Group." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TransitivePermutationGroup.html

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