Thread: subgroups

i'm sry, please delete.. or please inform me how to..?

Originally Posted by cowgirl123

H and K are finite subgroups of group G. |H| and |K| are relatively prime.
Prove (H intersects K) = {identity}

Let . Let . Then by Lagrange's theorem and . Since these are relatively prime it means . So must be .
Q.E.D.

i'm not sure how this proves that the intersection of H and K is equal to the identity?
Doesnt this just prove that the identity is in the set?

Originally Posted by cowgirl123

i'm not sure how this proves that the intersection of H and K is equal to the identity?
Doesnt this just prove that the identity is in the set?

I have shown that if an element is common to both subgroups then its order must be 1. But the only element with order 1 is the identity element. Thus the identity element is the only possible element common to both.