3
votes
1answer
55 views

Conjugation on subgroups of $A_4$ faithful?

Let $X$ be the set of all subgroups of $G=A_4$. We define the group action $$G\times X\ni(g,H)\mapsto gHg^{-1}\in X$$ I am trying to determine whether this action is faithful, i.e. $\bigcap_{H\in X} ...
1
vote
2answers
66 views

Finding the number of orbits

How many orbits are there of $(12)(25)$ in $S_{5}$? Considering the permutation $(12)$, it has $4$ orbits and is as follows: $\{\{1,2\},\{3\},\{4\},\{5\}\}$ and (25) also has 4 orbits and is also ...
5
votes
3answers
108 views

Group Action - Permutation on the Polynomial

I'm trying to check the permutation on the polynomial is a Group Action, but I'm not getting the second axiom. I'm following my lecturer's work --- Examples 2.1 and 2.6 on page 5 on ...