A group action ϕ:G×X->X is called faithful if there are no group elements g (except the identity element) such that g x = x for all x element X. Equivalently, the map ϕ induces an injection of G into the symmetric group S_X. So G can be identified with a permutation subgroup. Most actions that arise naturally are faithful. An example of an action which is not faithful is the action e^(i(x + y)) of G = R^2 = {(x, y)} on X = S^1 = {e^(i θ)}, i.e., ϕ(x, y, e^(i θ)) = e^(i(θ + x + y)).
We guarantee you’ll find the right tutor, or we’ll cover the first hour of your lesson.
Club Z! has connected me with a tutor through their online platform! This was exactly the one-on-one attention I needed for my math exam. I was very pleased with the sessions and ClubZ’s online tutoring interface.
My son was suffering from low confidence in his educational abilities. I was in need of help and quick. Club Z! assigned Charlotte (our tutor) and we love her! My son’s grades went from D’s to A’s and B’s.
I’ve been using Club Z’s online classrooms to receive some help and tutoring for 2 of my college classes. I must say that I am very impressed by the functionality and ease of use of their online App. Working online with my tutor has been a piece of cake. Thanks Z.
Jonathan is doing really well in all of his classes this semester, 5 A’s & 2 B’s (he has a computer essentials class instead of PLC). In his Algebra class that Nathan is helping him with he has an A+.
Sarah is very positive, enthusiastic and encourages my daughter to do better each time she comes. My daughter’s grade has improved, we are very grateful for Sarah and that she is tutoring our daughter. Way to go ClubZ!
