Thread: Stabilizers

Okay, just to make sure I have this straight:

Given a group G and an element g of G

The "stabilizer" of g is the subset such that for all .

And the stabilizer of g is a subgroup of G, right?

Thanks!
-Dan

Originally Posted by topsquark

Okay, just to make sure I have this straight:

Given a group G and an element g of G

The "stabilizer" of g is the subset such that for all .

And the stabilizer of g is a subgroup of G, right?

Thanks!
-Dan

You got the elements of the group confused with elements of the set.

Let be a a group, and let be a set. Let act on .
Given an element the stabalizer, , is the set . And yes, the stabalizer is a subgroup.

I can give some examples if you want to.

Originally Posted by ThePerfectHacker

You got the elements of the group confused with elements of the set.

Let be a a group, and let be a set. Let act on .
Given an element the stabalizer, , is the set . And yes, the stabalizer is a subgroup.

I can give some examples if you want to.

Ahhh! The lightbulb just went on. I think I've got it now. I'll play around with it a bit and let you know if I need more. Thanks!

-Dan