# Abstract Algebra

by Thorn
Tags: abstract, algebra
 P: 23 Geez...I have no idea where to start... Ok, I was looking at a lemma... "Let G be an abelian group and a $$\in$$ G and is an element of finite order. Then a = a1+a2+...+ak, with ai an element of G(pi), where p1,....,pk are the distinct positive primes that divide the order of a" .... now G(p) is only the set of all elements whose order is some power of p... I was thinking you could use that lemma to show that G(p) has power pt ...seems like that could help somehow.. but it seems I need to use the fact that (p,m)=1 ...this surely means that (pt,m)=1 which means you can write 1=pt*u + m*v...for some numbers u,v... and I have no idea where to go...