 Burnside's theorem states that if "G" is a finite group of order "paqb" where "p" and "q" are prime numbers, and "a" and "b" are non-negative integers, then "G" is solvable.As a strengthening of solvability, a group "G" is called supersolvable (or supersoluble) if it has an "invariant" normal series whose factors are all cyclic.Since a normal series has finite length by definition, uncountable groups are not supersolvable.