Hello,
...
is that cool?
Dummit and Foote Section 1.7 Group Actions - Exercise 4 is as follows:
Let G be a group acting on a set A and fix some a A.
Show that the following sets are subgroups of G:
(a) the kernel of the action
(b) {g G | ga = a} {stabilizer of a in G}
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I am working on part (a) and have not got far!
We know that the kernel of the action of G on A is as follows:
Kernel, K = {g G| ga = a for all a A}
We need to show x K for all x, y K
So assume , K
Then a = a and a = a
Now need to show K
That is ( )a = a
Now ( )a = ( a)
But ??? where to from here
Can anyone help? Be grateful for some assistance!
Peter