1. The problem statement, all variables and given/known data Show that if a belongs to G where G is finite with identity e, then there exists a positive n such that a^n = e 2. Relevant equations 3. The attempt at a solution Someone tell me if i am reasoning correctly. Suppose a^n is not equal to e. By finiteness of G, a^n = b for some b belonging to G. Then b^t = (a^n)^t is not equal to e for any positive t. so G is infinite? i dunno i am stuck.