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 . 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