1. The problem statement, all variables and given/known data I have recently started a new course in Algebra. I have to proof that if S is a subset of a finite group G, with an order greater than half the order of G, S is a generating subset for G. 2. Relevant equations I haven't had cosets nor Lagrange theorem so I suppose I should try to prove it from scratch. 3. The attempt at a solution I have put my mind to the problem for a while now but didnt come up with any meaningful clues. I would be very thankful for any tips.