State and prove the orbit-stabilizer theorem. Deduce that if is an element of a finite group then the order of divides the order of
Prove Cauchy's theorem, that if is a prime dividing the order of a finite group then contains an element of order .
For which positive integers does there exist a group of order in which every element (apart from the identity) has order 2?
Give an example of an infinite group in which every element (apart from the identity) has order