Exercises through show how all possible G-sets, up to isomorphism (see Exercise 9), can be formed from the group G. Let {Xi | i ∈ I} be a disjoint collection of sets, so Xi, ∩ Xj = ∅ for i ≠ j. Let each Xi be a G-set for the same group G.
a. Show that ∪i∈Xi can be viewed in a natural way as a G-set, the union of the G-sets Xi.
b. Show that every G-set X is the union of its orbits.
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.