Editing Group action (section)

==== Examples ====
The action of the symmetric group of {{math|''X''}} is transitive, in fact {{math|''n''}}-transitive for any {{math|''n''}} up to the cardinality of {{math|''X''}}. If {{math|''X''}} has cardinality {{math|''n''}}, the action of the [[alternating group]] is {{math|(''n'' − 2)}}-transitive but not {{math|(''n'' − 1)}}-transitive.

The action of the [[general linear group]] of a vector space {{math|''V''}} on the set {{math|''V'' &setminus; {{mset|0}}}} of non-zero vectors is transitive, but not 2-transitive (similarly for the action of the [[special linear group]] if the dimension of {{math|''v''}} is at least 2). The action of the [[orthogonal group]] of a Euclidean space is not transitive on nonzero vectors but it is on the [[unit sphere]].