Originally Posted by
ChrisBickle Heres the question:
Let G be a group a element in G and H is a subgroup of G. Define K={aha(inverse) such that h element in H. Prove K is a subgroup of G.
Heres what i got.
Let x,y elements in K then there exists c,d elements in H such that x=aca(inverse) and y = ada(inverse). then xy equals (aca(inverse))(ada(inverse)) group the a and a inverse in the middle to get a(cd)a(inverse) c,d elements in H so thats in K.
This is where i get stuck. We know the identity is in H because H subgroup of G how do we show e is in K. Also how do we find the inverse of this and prove its in K.