A group action G×X->X is transitive if it possesses only a single group orbit, i.e., for every pair of elements x and y, there is a group element g such ...

Now we turn to examples (and non-examples) of transitive actions using abstract groups. Example 2.5. Let a group G act on itself by left multiplication.

6 авг. 2015 г. · Illustration: Imagine that X X is a little box of marbles resting on the floor of a room Y Y , and let G G act on Y Y so that all the elements ...

6 сент. 2015 г. · The group action is transitive if and only if it has only one orbit, ie if there exists x∈X with G⋅x=X. This is the case if and only if G⋅x=X for all x∈X. Intuitive meaning of transitive action - Math Stack Exchange What does "transitive" mean in group action? Transitivity of group actions - examples abstract algebra - Intuitive meaning of transitive group action. Другие результаты с сайта math.stackexchange.com

The group action is transitive if and only if it has exactly one orbit, that ... Isometries are in fact one example of affine group (action). Definition · Notable properties of actions · Examples

19 окт. 2015 г. · The phrase, "a group action is transitive" is just the mathematician's way of saying "Where there's a will, there's a way!"

12 мая 2024 г. · An action of ℤ \mathbb{Z} (viewed as the free group on one generator) on a set X X corresponds to an arbitrary permutation π : X → X \pi : X \to ... Definition · Examples · As an action on cosets

22 июл. 2020 г. · The group action is transitive if and only if for any x,y∈S there exists g∈G such that g∗x=y.

7 июн. 2020 г. · Namely, a permutation group (G,X) is said to be 1/2- transitive if either |X|=1, or if all orbits of (G,X) have the same length greater than 1.

Examples. Every group is trivially 1-transitive, by its action on itself by left-multiplication. , then the action is sharply n-transitive.