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'd like to prove group $G$ is simple if and only if for every pair $g,h \in G$ ($g \ne 1$), $h$ can always be written product of finite number conjugates of $g$ and $g^{-1}$.

share|cite|improve this question
Have you shown implication in one of the directions? If $G$ has some non-trivial proper normal subgroup, can you find elements $g$ and $h$ not satisfying the given? – Tobias Kildetoft Oct 14 '13 at 12:19
Your question would likely attract more positive attention if you said what you'd tried to do to work out the answer for yourself (or where you're stuck). – TooTone Oct 14 '13 at 12:34

Hint: look at the subgroup of $G$ generated by the conjugacy class of $g \in G$ and observe that this subgroup is normal.

share|cite|improve this answer
Nice, simple and short accurate hint. +1 – DonAntonio Oct 14 '13 at 12:43

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.