Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have a proof, but I wonder known another proofs. My proof:
Let $H\leq G$ be a subgroup of $G$. Let $H$ act on the coset space $(G/H)\setminus\{H\}$. By the orbit-stab.theorem and the assumption, you can easily see that all orbits of the coset space are singletons. If we define the action rule $h.gH=hgH$ , we get that $H$ is normal.

share|cite|improve this question
There may be something of interest at…? In any event, I'm sure the question has been discussed on this site before. It may be worthwhile to search for it a bit, starting with the Related questions running down the right side of this page. – Gerry Myerson Nov 30 '12 at 21:58
Here is basically a duplicate. – JSchlather Nov 30 '12 at 22:09

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.