kenrnal of a map for group action
Okay, given a function for a group action of the group G acting on a set A (with a fixed point a of A): 
. One definition I have for the kernal is  | \phi _a (g, a) = 1_A ~ \forall g \in G \})
. But the definition in the group action section is that 
. Are these somehow equivalent? I don't see it.
-Dan
Re: kenrnal of a map for group action
I don't understand the definition of 
. If a is a fixed point of G, then g.a=a for all g. So what is )
for 
Re: kenrnal of a map for group action
Quote:
Originally Posted by
Haven 
I don't understand the definition of
. If a is a fixed point of G, then g.a=a for all g. So what is
for
In general the group action of a group G acting on an element of a set A is defined as 
. The group G essentially acts as a permutation on the set A. If we restrict ourselves to a fixed element a of A (not G) then we have . My question is how to define the kernal of 
.
-Dan
